A236111 -id:A236111

Search: a236111 -id:a236111

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A236102

Numbers whose divisors are partition numbers.

+10
6

1, 2, 3, 5, 7, 11, 15, 22, 77, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557, 74878248419470886233, 1394313503224447816939

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

OFFSET

1,2

COMMENTS

By definition all terms are partition numbers.

All members of A049575 are in this sequence.

Conjecture: the only composite numbers in this sequence are 15, 22, and 77. - Jon E. Schoenfield, Feb 05 2014

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

15 is in the sequence because the divisors of 15 are 1, 3, 5, 15, which are also partition numbers.

CROSSREFS

Cf. A000041, A027750, A049575, A236103, A236105, A236107, A236108, A236110, A236111.

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 21 2014

EXTENSIONS

More terms from Jon E. Schoenfield, Feb 05 2014

STATUS

approved

A236110

Smallest number with the property that exactly n of its divisors are partition numbers.

+10
5

1, 2, 6, 15, 42, 30, 270, 210, 462, 1848, 3696, 11088, 2310, 9240, 18480, 55440, 83160, 166320, 498960, 2494800, 17463600, 331808400, 4418290800

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

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

a(3) = 6 because 6 is the smallest number with the property that exactly three of its divisors are partition numbers. The divisors of 6 are 1, 2, 3, 6, and 1, 2, 3 are also partition numbers.

a(5) = 42 because 42 is the smallest number with the property that exactly five of its divisors are partition numbers. The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42, and 1, 2, 3, 7, 42 are members of A000041.

CROSSREFS

Cf. A000041, A236102, A236103, A236105, A236107, A236108, A236111.

KEYWORD

nonn,more,hard

AUTHOR

Omar E. Pol, Jan 22 2014

EXTENSIONS

a(12) and a(15)-a(18) from Alois P. Heinz, Jan 22 2014

a(19)-a(22) from Giovanni Resta, Feb 06 2014

a(23) from Amiram Eldar, Jun 23 2023

STATUS

approved

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