A112581 Number of partitions of n into 5-smooth parts.

1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 50, 69, 87, 115, 146, 189, 235, 302, 371, 469, 575, 714, 867, 1072, 1292, 1577, 1894, 2293, 2734, 3293, 3902, 4664, 5511, 6542, 7690, 9094, 10638, 12507, 14588, 17073, 19830, 23121, 26757, 31066, 35860, 41469, 47701

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Smooth Number

Eric Weisstein's World of Mathematics, Partition Function P

Formula

G.f.: Product_{a>=0} Product_{b>=0} Product_{c>=0} 1/(1-x^(2^a*3^b*5^c)). - Robert Israel, Apr 16 2019

Maple

N:= 100:
P:= select(t -> max(numtheory:-factorset(t))<=5, [$1..N]):
S:= series(mul(1/(1-q^k), k=P), q, N+1):
seq(coeff(S, q, k), k=1..N); # Robert Israel, Apr 16 2019

Crossrefs

Cf. A000041, A051037, A105420, A112582.

Sequence in context: A023027 A051014 A035968 * A288255 A325853 A035976

Adjacent sequences: A112578 A112579 A112580 * A112582 A112583 A112584

Keyword

nonn

Author

Reinhard Zumkeller, Sep 14 2005

Status

approved