A286224 Number of compositions (ordered partitions) of n into parts with an odd number of distinct prime divisors.

1, 0, 1, 1, 2, 3, 4, 8, 11, 19, 28, 47, 72, 116, 182, 289, 460, 724, 1153, 1820, 2891, 4572, 7249, 11482, 18190, 28821, 45651, 72338, 114582, 181549, 287597, 455647, 721849, 1143590, 1811753, 2870247, 4547245, 7203933, 11412922, 18080907, 28644799, 45380602, 71894401, 113899027, 180444897, 285870668

Offset

0,5

Links

Amiram Eldar, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A030230(k)).

Example

a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].

Mathematica

nmax = 45; CoefficientList[Series[1/(1 - Sum[Boole[OddQ[PrimeNu[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A030230, A285799, A286220, A286225.

Sequence in context: A046812 A269797 A280195 * A361313 A245388 A164573

Adjacent sequences: A286221 A286222 A286223 * A286225 A286226 A286227

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved