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
Keywords
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
Programs
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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