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

Author

Reinhard Zumkeller, Sep 14 2005

Keywords

• nonn

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

Crossrefs

Cf. A000041, A051037, A105420, A112582.

Programs

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

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