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

1,2

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

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]

Formula

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

Example

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

Mathematica

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

Prog

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

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]

Sequence in context: A098929 A073098 A201267 * A336876 A083664 A083125

Adjacent sequences: A046638 A046639 A046640 * A046642 A046643 A046644

Keyword

nonn

Author

David W. Wilson

Extensions

Definition corrected by Max Alekseyev, Apr 25 2010

Status

approved