A072871 Smallest partition number divisible by n.

1, 2, 3, 56, 5, 30, 7, 56, 135, 30, 11, 792, 3718, 42, 15, 176, 386155, 792, 627, 715220, 42, 22, 8349, 792, 1575, 3718, 135, 56, 2436, 30, 75175, 2323520, 231, 92669720, 385, 792, 34262962, 124754, 4835271870, 2323520, 14883, 42, 3010, 176, 135, 8118264, 526823

Offset: 1

Author

Benoit Cloitre, Jul 28 2002

Keywords

• easy
• nonn
• look

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PARI program for this sequence

Programs

PARI

a(n) = {my(k=1,pk); while((pk=numbpart(k)) % n, k++); pk;} \\ Michel Marcus, Nov 26 2013

Python

from sympy import npartitions
def a(n):
    k = 1
    while npartitions(k)%n: k += 1
    return npartitions(k)
print([a(n) for n in range(1, 48)]) # Michael S. Branicky, Aug 05 2022

Formula

a(n) = n*A235704(n). - Omar E. Pol, Jan 15 2014