OFFSET
0,9
EXAMPLE
a(12) = 4 because we have [6, 6], [4, 4, 4], [4, 4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 66; CoefficientList[Series[Product[1 + Boole[!PrimeQ[k]] x^(2 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Table[Count[IntegerPartitions[n], _?(NoneTrue[#, PrimeQ]&&Min[Length/@Split[#]]>1&)], {n, 0, 70}] (* Harvey P. Dale, Oct 03 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 27 2020
STATUS
approved