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A105420 Number of partitions of n into 3-smooth parts.

%I A105420 #19 Oct 13 2021 12:47:23
%S A105420 1,1,2,3,5,6,10,12,18,23,31,38,53,63,82,100,128,152,194,228,284,336,
%T A105420 410,478,586,678,814,947,1127,1296,1539,1761,2070,2372,2764,3146,3667,
%U A105420 4153,4796,5437,6249,7044,8080,9080,10358,11636,13208,14778,16762,18698
%N A105420 Number of partitions of n into 3-smooth parts.
%C A105420 See A062051 for partitions into distinct 3-smooth numbers.
%H A105420 Alois P. Heinz, <a href="/A105420/b105420.txt">Table of n, a(n) for n = 0..10000</a> (first 121 terms from Jean-François Alcover)
%F A105420 A117222(n) = a(A003586(n)). - _Reinhard Zumkeller_, Mar 04 2006
%e A105420 n=10: there are 11 partitions of 10 with at least one part not of the form 2^i*3^j: 10, 7+3, 7+2+1, 7+1+1+1, 5+5, 5+4+1, 5+3+2, 5+3+1+1, 5+2+2+1, 5+2+1+1+1 and 5+1+1+1+1+1, therefore a(10) = A000041(10) - 11 = 42 - 11 = 31.
%t A105420 nmax = 120;
%t A105420 S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
%t A105420 P[n_] := IntegerPartitions[n, All, TakeWhile[S, # <= n &] ];
%t A105420 a[n_] := a[n] = P[n] // Length;
%t A105420 Table[Print[n, " ", a[n]]; a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Oct 13 2021 *)
%Y A105420 Cf. A000041, A003586.
%Y A105420 Cf. A117220, A117221.
%Y A105420 Cf. A062051, A023893, A131995.
%K A105420 nonn
%O A105420 0,3
%A A105420 _Reinhard Zumkeller_, Apr 07 2005