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%I #6 Apr 16 2019 21:43:55
%S 1,2,3,5,7,11,14,21,28,39,50,69,87,115,146,189,235,302,371,469,575,
%T 714,867,1072,1292,1577,1894,2293,2734,3293,3902,4664,5511,6542,7690,
%U 9094,10638,12507,14588,17073,19830,23121,26757,31066,35860,41469,47701
%N Number of partitions of n into 5-smooth parts.
%H Robert Israel, <a href="/A112581/b112581.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%F 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
%p N:= 100:
%p P:= select(t -> max(numtheory:-factorset(t))<=5, [$1..N]):
%p S:= series(mul(1/(1-q^k),k=P),q,N+1):
%p seq(coeff(S,q,k),k=1..N); # _Robert Israel_, Apr 16 2019
%Y Cf. A000041, A051037, A105420, A112582.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Sep 14 2005
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