A286227 Number of compositions (ordered partitions) of n into parts with an even number of prime divisors (counted with multiplicity).
1, 1, 1, 1, 2, 3, 5, 7, 10, 15, 24, 36, 53, 78, 118, 179, 271, 405, 605, 907, 1366, 2055, 3086, 4628, 6948, 10440, 15689, 23560, 35371, 53110, 79771, 119821, 179958, 270243, 405833, 609495, 915394, 1374780, 2064647, 3100680, 4656676, 6993575, 10503180, 15773877, 23689467, 35577360
Offset: 0
Keywords
Examples
a(6) = 5 because we have [6], [4, 1, 1], [1, 4, 1], [1, 1, 4] and [1, 1, 1, 1, 1, 1].
Links
- Amiram Eldar, Table of n, a(n) for n = 0..5000
- Eric Weisstein's World of Mathematics, Prime Factor
- Index entries for sequences related to compositions
Programs
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Mathematica
nmax = 45; CoefficientList[Series[1/(1 - Sum[Boole[EvenQ[PrimeOmega[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
Formula
G.f.: 1/(1 - Sum_{k>=1} x^A028260(k)).