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

1,4

Comments

a(n) = 1 iff n is a partition number.

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = A072871(n)/n.

Example

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.

Mathematica

a[n_] := PartitionsP[NestWhile[(# + 1)&, 1, Mod[PartitionsP@ #, n] > 0 &]]/n; Array[a, 51] (* Giovanni Resta, Jan 15 2014 *)

Crossrefs

Cf. A000041, A046641, A072871, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225361.

Sequence in context: A040203 A040205 A171693 * A229199 A040206 A040207

Adjacent sequences: A235701 A235702 A235703 * A235705 A235706 A235707

Keyword

nonn

Author

Omar E. Pol, Jan 14 2014

Status

approved