A286222 Number of partitions of n into distinct parts with an odd number of prime divisors (counted with multiplicity).
1, 0, 1, 1, 0, 2, 0, 2, 2, 1, 3, 2, 3, 4, 3, 5, 4, 5, 7, 6, 10, 8, 10, 12, 10, 15, 14, 16, 20, 18, 25, 25, 28, 32, 31, 38, 38, 44, 49, 51, 59, 61, 68, 75, 79, 89, 93, 103, 113, 120, 137, 141, 157, 168, 176, 200, 205, 229, 245, 260, 289, 303, 332, 356, 376, 411, 433, 470, 507, 535, 587
Offset: 0
Keywords
Examples
a(10) = 3 because we have [8, 2], [7, 3] and [5, 3, 2].
Links
- Amiram Eldar, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Prime Factor
- Index entries for related partition-counting sequences
Programs
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Mathematica
nmax = 70; CoefficientList[Series[Product[1 + Boole[OddQ[PrimeOmega[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=1} (1 + x^A026424(k)).