Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Nov 28 2020 20:03:39
%S 1,0,1,1,2,1,4,2,6,5,9,7,15,11,21,19,31,27,46,40,63,60,88,83,124,117,
%T 166,165,224,222,303,301,399,407,525,537,691,707,893,929,1153,1202,
%U 1485,1550,1890,1992,2400,2534,3040,3212,3818,4059,4781,5089,5972,6359,7412
%N Number of partitions of n into prime power parts (including 1) where every part appears at least 2 times.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: (1 + x^2 / (1 - x)) * Product_{p prime, k>=1} (1 + x^(2*p^k) / (1 - x^(p^k))).
%e a(6) = 4 because we have [3, 3], [2, 2, 2], [2, 2, 1, 1] and [1, 1, 1, 1, 1, 1].
%t nmax = 56; CoefficientList[Series[(1 + x^2/(1 - x)) Product[1 + Boole[PrimePowerQ[k]] x^(2 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000961, A007690, A023893, A161077, A339218, A339242.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Nov 28 2020