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A112581 Number of partitions of n into 5-smooth parts. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 16:12 EDT 2022. Contains 353747 sequences. (Running on oeis4.)