A339242 Number of partitions of n into prime power parts (1 excluded) where every part appears at least 2 times.

1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 3, 0, 5, 1, 6, 3, 9, 2, 12, 4, 15, 8, 21, 8, 28, 13, 34, 20, 45, 23, 59, 34, 73, 47, 92, 57, 119, 78, 145, 103, 182, 128, 229, 166, 277, 213, 344, 265, 427, 334, 513, 420, 629, 517, 771, 641, 923, 794, 1120, 967, 1355, 1182, 1618, 1447, 1946, 1745

Offset

0,7

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to partitions

Formula

G.f.: Product_{p prime, k>=1} (1 + x^(2*p^k) / (1 - x^(p^k))).

Example

a(12) = 5 because we have [4, 4, 4], [4, 4, 2, 2], [3, 3, 3, 3], [3, 3, 2, 2, 2] and [2, 2, 2, 2, 2, 2].

Mathematica

nmax = 65; CoefficientList[Series[Product[1 + Boole[PrimePowerQ[k]] x^(2 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A007690, A023894, A161077, A246655, A339218, A339241.

Sequence in context: A082023 A349438 A078152 * A339222 A191247 A308263

Adjacent sequences: A339239 A339240 A339241 * A339243 A339244 A339245

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 28 2020

Status

approved