A245802 -id:A245802

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A241989

Positive numbers n that are divisible by the sum of the digits of n in base 16.

+10
2

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32, 33, 35, 36, 40, 45, 48, 50, 54, 60, 64, 65, 66, 70, 72, 75, 80, 90, 96, 99, 100, 105, 108, 112, 120, 126, 128, 130, 132, 135, 140, 144, 150, 160, 165, 175, 176, 180, 192, 195, 198, 200

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

A base 16 version of Harshad (or Niven) numbers (A005349).

Numbers n such that n = 0 modulo A053836(n). - Antti Karttunen, Aug 22 2014

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

82478 is in the sequence as it is 1422E in hexadecimal and 1+4+2+2+14 = 23 which divides 82478.

MATHEMATICA

Select[Range[200], Divisible[#, Total@ IntegerDigits[#, 16]] &] (* Indranil Ghosh, Jun 12 2017 *)

PROG

(Python)

from gmpy2 import digits

A241989 = [n for n in range(1, 10**3) if not n % sum([int(d, 16) for d in digits(n, 16)])]

(MIT/GNU Scheme, with Antti Karttunen's IntSeq-library)

(define A241989 (MATCHING-POS 1 1 (lambda (n) (zero? (modulo n (A053836 n))))))

(define (A053836 n) (let loop ((n n) (i 0)) (if (zero? n) i (loop (floor->exact (/ n 16)) (+ i (modulo n 16))))))

CROSSREFS

Cf. A005349, A053836, A245802.

KEYWORD

nonn,base

AUTHOR

Chai Wah Wu, Aug 22 2014

STATUS

approved

A325309

Square array read by downward antidiagonals: A(n, k) is the k-th Niven number (or Harshad number) in base n.

+10
0

1, 2, 1, 4, 2, 1, 6, 3, 2, 1, 8, 4, 3, 2, 1, 10, 6, 4, 3, 2, 1, 12, 8, 6, 4, 3, 2, 1, 16, 9, 8, 5, 4, 3, 2, 1, 18, 10, 9, 6, 5, 4, 3, 2, 1, 20, 12, 12, 8, 6, 5, 4, 3, 2, 1, 21, 15, 16, 10, 10, 6, 5, 4, 3, 2, 1, 24, 16, 18, 12, 12, 7, 6, 5, 4, 3, 2, 1, 32, 18

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Table of n, a(n) for n=2..81.

Wikipedia, Harshad number

EXAMPLE

The array starts as follows:

1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 21, 24, 32, 34, 36, 40, 42, 48, 55, 60

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32

1, 2, 3, 4, 5, 6, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 42, 44, 45, 48

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14, 15, 16, 18, 21, 24, 27, 28, 30, 32

1, 2, 3, 4, 5, 6, 7, 8, 14, 16, 21, 24, 28, 32, 35, 40, 42, 48, 49, 56

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 35

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 22, 24, 33, 36, 44, 48, 55, 60

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 24, 26, 27

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 26, 28, 39, 42, 52, 56

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 21, 28, 30, 32

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 30, 32

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 24

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34, 36

PROG

(PARI) row(n, terms) = my(i=0); for(x=1, oo, if(i >= terms, break); if(x%sumdigits(x, n)==0, print1(x, ", "); i++))

array(rows, cols) = for(x=2, rows+1, row(x, cols); print(""))

array(18, 20) \\ Print initial 18 rows and 20 columns of array

CROSSREFS

Cf. A049445 (row 2), A064150 (row 3), A064438 (row 4), A064481 (row 5), A245802 (row 8), A005349 (row 10).

Cf. A005349.

KEYWORD

nonn,tabl,base,easy

AUTHOR

Felix Fröhlich, Sep 06 2019

STATUS

approved

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