Moran numbers

A number

is a Moran number if $n$

divided by the sum of its digits gives a prime number.

For example, 111 is a Moran number because 111/(1+1+1) = 37 and 37 is a prime number.

Moran numbers are a subset of Harshad numbers.

The first pair of consecutive Moran numbers is (152, 153, while the first runs of length 3, 4, 5 and 6 start at 3031, 21481224, 25502420, and 4007565001480, respectively. For this last value we have

$\begin{array}{ll} 4007565001480 =& 40\cdot 100189125037\\ 4007565001481 =& 41\cdot 97745487841\\ 4007565001482 =& 42\cdot 95418214321\\ 4007565001483 =& 43\cdot 93199186081\\ 4007565001484 =& 44\cdot 91081022761\\ 4007565001485 =& 45\cdot 89057000033 \end{array}$

(I found this number in October 2010: let me know if it appeared somewhere before.)

The first Moran numbers are 18, 21, 27, 42, 45, 63, 84, 111, 114, 117, 133, 152, 153, 156, 171, 190, 195, 198, 201, 207, 209, 222, 228 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many Moran numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.

Useful links OEIS, Sequence A001101

Moran numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 18 aban 18 21 27 + 99000756 abundant 18 42 84 + 49999734 admirable 42 84 114 + 99500212 alternating 18 21 27 + 98989074 amenable 21 45 84 + 99999965 anti-perfect 285 apocalyptic 222 247 285 + 29984 arithmetic 21 27 42 + 9999950 astonishing 27 betrothed 195 binomial 21 45 84 + 666 brilliant 21 209 247 + 1679 c.decagonal 3781 50501 102961 + 94156301 c.heptagonal 19426 105358 1801822 + 95716846 c.nonagonal 190 c.pentagonal 29431 189751 409051 + 92461606 c.square 481 26221 82825 + 98434481 c.triangular 2710 22510 135451 + 95676274 cake 42 Catalan 42 congruent 21 45 63 + 9999950 cube 27 Cunningham 63 195 399 + 99920017 Curzon 18 21 114 + 99999965 cyclic 133 209 247 + 9999881 D-number 21 63 111 + 2000001 d-powerful 63 153 209 + 9998252 de Polignac 4311 10963 14383 + 99987085 decagonal 27 370 1387 deceptive 481 66991 12345679 deficient 21 27 45 + 9999950 dig.balanced 21 42 114 + 95454108 Duffinian 21 27 63 + 9999881 eban 42 4044 6062 + 66002060 economical 21 27 111 + 19999709 emirpimes 511 629 1011 + 99992171 enlightened 29090912 equidigital 21 27 111 + 19999709 eRAP 3438 esthetic 21 45 12345 + 98767678 Eulerian 247 evil 18 27 45 + 99999699 fibodiv 23418 927267 38304312 43092351 Fibonacci 21 Friedman 153 1503 12102 + 976572 gapful 190 195 198 + 59998914 Gilda 152 30254 happy 133 190 888 + 9999802 Harshad 18 21 27 + 99999965 heptagonal 18 1651 hex 1141 1387 3781 + 92524087 hexagonal 45 153 190 hoax 84 516 645 + 99957093 Hogben 21 111 133 + 99390931 house 6308092 7008923 15777182 27994726 hyperperfect 21 iban 21 27 42 + 777411 idoneal 18 21 42 + 190 inconsummate 63 84 195 + 999036 insolite 111 interprime 18 21 42 + 99999965 Jacobsthal 21 171 junction 111 117 511 + 99997362 Kaprekar 45 999 5555556 katadrome 21 42 63 + 87543210 Lehmer 133 247 481 + 98205733 Leyland 16580 lonely 1341 Lucas 18 lucky 21 63 111 + 9999283 Lynch-Bell 1236 1926 1962 + 864312 magic 111 3439 23346 magnanimous 21 152 209 + 62202281 metadrome 18 27 45 + 12345679 modest 111 133 209 + 99036585 Motzkin 21 narcissistic 153 370 407 9926315 nialpdrome 21 42 63 + 99999965 nonagonal 111 261 7944 nude 111 222 333 + 99919926 O'Halloran 84 156 oban 18 27 63 + 999 octagonal 21 133 481 645 odious 21 42 84 + 99999965 palindromic 111 171 222 + 89888898 pancake 407 10012 16654 + 98511667 panconsummate 18 21 45 + 3097 pandigital 21 114 156 + 95454108 partition 42 pentagonal 117 247 1926 pernicious 18 21 42 + 9999950 Perrin 209 963935 plaindrome 18 27 45 + 56666699 Poulet 645 1387 1905 power 27 powerful 27 practical 18 42 84 + 888 prim.abundant 18 42 114 + 99500212 primeval 10279 12345679 pronic 42 156 Proth 209 481 801 + 99368961 pseudoperfect 18 42 84 + 999612 repdigit 111 222 333 + 999 repunit 21 63 111 + 99390931 Ruth-Aaron 153 370 self 42 198 209 + 99999963 self-describing 12173133 12311733 15143331 + 33253225 semiprime 21 111 133 + 99993563 sliding 133 15689 90925 1563140 Smith 27 645 666 + 99957093 sphenic 42 114 190 + 99999965 star 2986381 6875821 7359337 + 97711561 straight-line 111 222 333 + 12345 strobogrammatic 111 888 1001001 + 61996619 subfactorial 1854 super-d 190 247 261 + 9999881 tau 18 84 152 + 99960012 tetrahedral 84 triangular 21 45 153 + 666 trimorphic 999 uban 18 21 27 + 96000039 Ulam 18 114 209 + 10000236 undulating 171 1818 13131 + 73737 unprimeable 516 518 846 + 9999950 untouchable 372 516 518 + 999548 upside-down 555 53575 58525 5565455 wasteful 18 42 45 + 9999950 Wieferich 22953 Woodall 63 4607 Zuckerman 111 11133 11331 + 13111212 Zumkeller 42 84 114 + 99930 zygodrome 111 222 333 + 99966699