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A046641
a(n) is the smallest positive integer m such that the number of partitions p(m) = A000041(m) is divisible by n.
10
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
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
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
KEYWORD
nonn
EXTENSIONS
Definition corrected by Max Alekseyev, Apr 25 2010
STATUS
approved