A286221 Number of partitions of n into distinct parts with an even number of distinct prime divisors.
1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 6, 5, 5, 6, 7, 9, 10, 10, 12, 11, 11, 15, 16, 15, 17, 18, 19, 23, 26, 25, 27, 30, 33, 37, 38, 39, 46, 50, 52, 57, 59, 61, 71, 77, 78, 84, 91, 97, 107, 114, 120, 131, 139, 147, 163, 172, 180, 197
Offset: 0
Keywords
Examples
a(21) = 4 because we have [21], [20, 1], [15, 6] and [14, 6, 1].
Links
- Amiram Eldar, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Distinct Prime Factors
- Index entries for related partition-counting sequences
Programs
-
Mathematica
nmax = 75; CoefficientList[Series[Product[1 + Boole[EvenQ[PrimeNu[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Product_{k>=1} (1 + x^A030231(k)).