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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
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 14 2005
STATUS
approved