A046641 a(n) is the smallest positive integer m such that the number of partitions p(m) = A000041(m) is divisible by n.

1, 2, 3, 11, 4, 9, 5, 11, 14, 9, 6, 21, 28, 10, 7, 15, 54, 21, 20, 58, 10, 8, 32, 21, 24, 28, 14, 11, 26, 9, 44, 66, 16, 94, 18, 21, 86, 47, 129, 66, 35, 10, 27, 15, 14, 75, 56, 70, 19, 74, 178, 62, 52, 340, 18, 11, 20, 26, 54, 124, 115, 101, 24, 66, 84, 21, 47, 94, 32, 19

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

The initial term could also be taken to be 0.

From the formula a(p(n)) = n, it follows that every positive integer appears in this sequence. - Franklin T. Adams-Watters, Feb 09 2016

Examples

			The first partition number divisible by 9 is p(14) = 135, so a(9) = 14.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..20000.
• M. F. Hasler, A046641.c - C program for fast computation of a(n) for large values of n. [From _M. F. Hasler_, Oct 18 2008]

Crossrefs

Cf. A000041, A040051.

See A091690 for simple PARI code, A145523(n)=a(2^n), A145524(n)=a(10^n), A145771 for record values. [M. F. Hasler, Oct 18 2008]

Programs

Mathematica

Table[SelectFirst[Range[10^3], Divisible[PartitionsP@ #, n] &], {n, 70}] (* Michael De Vlieger, Feb 10 2016, Version 10 *)

PARI

a(n) = my(m = 1); while(numbpart(m) % n, m++); m; \\ Michel Marcus, Feb 10 2016

Formula

a(p(n)) = n. - Franklin T. Adams-Watters, Feb 09 2016

Extensions

Definition corrected by Max Alekseyev, Apr 25 2010