A235704 a(n) is the smallest number k such that n*k is a partition number.
1, 1, 1, 14, 1, 5, 1, 7, 15, 3, 1, 66, 286, 3, 1, 11, 22715, 44, 33, 35761, 2, 1, 363, 33, 63, 143, 5, 2, 84, 1, 2425, 72610, 7, 2725580, 11, 22, 926026, 3283, 123981330, 58088, 363, 1, 70, 4, 3, 176484, 11209, 85166, 10, 141790, 11209835405
Offset: 1
Keywords
Examples
For n = 4, a(4) = 14 because if 1 <= k <= 13 we have that 4*k is not a partition number, but if k = 14 then 4*14 = 56 and 56 is the number of partitions of 11.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
a[n_] := PartitionsP[NestWhile[(# + 1)&, 1, Mod[PartitionsP@ #, n] > 0 &]]/n; Array[a,51] (* Giovanni Resta, Jan 15 2014 *)
Formula
a(n) = 1 iff n is a partition number.
a(n) = A072871(n)/n.