OFFSET
0,31
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Semiprime
FORMULA
G.f.: Product_{k>=1} 1/(1 - floor(bigomega(2*k+1)/2)*floor(2/bigomega(2*k+ 1))*x^(2*k+1)), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).
EXAMPLE
a(39) = 3 because we have [39], [21, 9, 9] and [15, 15, 9].
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[1/(1 - Floor[PrimeOmega[2 k + 1]/2] Floor[2/PrimeOmega[2 k + 1]] x^(2 k + 1)), {k, 1, nmax}], {x, 0, nmax}], x]
Join[{1}, Table[Count[IntegerPartitions[n], _?(AllTrue[#, OddQ]&&Union[PrimeOmega[#]]=={2}&)], {n, 110}]] (* Harvey P. Dale, Nov 11 2024 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Ilya Gutkovskiy, Jan 10 2017
STATUS
approved