A339242 - OEIS

%I #5 Nov 28 2020 20:03:48

%S 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,

%T 59,34,73,47,92,57,119,78,145,103,182,128,229,166,277,213,344,265,427,

%U 334,513,420,629,517,771,641,923,794,1120,967,1355,1182,1618,1447,1946,1745

%N Number of partitions of n into prime power parts (1 excluded) 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.: Product_{p prime, k>=1} (1 + x^(2*p^k) / (1 - x^(p^k))).

%e 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].

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

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

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Nov 28 2020