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%I #15 Oct 13 2021 08:27:42
%S 1,2,3,5,11,22,30,77,231,385,1575,3010,8349,17977,147273,386155,
%T 1741630,5392783,18004327,118114304,483502844,4351078600,22540654445,
%U 129913904637,1987276856363,15285151248481,133978259344888,365749566870782,3925922161489422,49005643635237875
%N Number of partitions of 3-smooth numbers.
%H Andrew Howroyd, <a href="/A117221/b117221.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = A000041(A003586(n)).
%t PartitionsP /@ Select[Range[1000], AllTrue[FactorInteger[#][[All, 1]], # <= 3 &] &] (* _Jean-François Alcover_, Oct 13 2021 *)
%o (PARI) \\ here is(n) is test for A003586 inclusion.
%o is(n)={forprime(p=2, 3, n/=p^valuation(n,p)); n==1}
%o seq(n)={my(A=List(), i=0); while(#A<n, i++; if(is(i), listput(A, numbpart(i)))); Vec(A)} \\ _Andrew Howroyd_, Jan 02 2020
%Y Cf. A000041, A003586, A090184, A117220, A117222.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Mar 04 2006
%E More terms from _Michel Marcus_, Apr 20 2019
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