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%I #30 Sep 30 2018 02:36:02
%S 1,1,1,2,1,5,1,4,3,8,1,16,1,11,11,8,1,33,1,26,15,17,1,56,5,20,9,36,1,
%T 226,1,16,23,26,23,120,1,29,27,92,1,422,1,56,78,35,1,208,7,140,35,66,
%U 1,261,35,128,39,44,1,1487,1,47,108,32,41,996,1,86,47,1062,1,456,1,56
%N Number of partitions of n in its prime divisors with at least one part of size 1.
%H Antti Karttunen, <a href="/A014652/b014652.txt">Table of n, a(n) for n = 1..10000</a>
%H David A. Corneth, <a href="/A014652/a014652.txt">PARI program</a>
%F Coefficient of x^(n-1) in expansion of (1/(1-x))*1/Product_{d is prime divisor of n} (1-x^d). - _Vladeta Jovovic_, Apr 11 2004
%o (PARI)
%o \\ This is for computing just a moderate number of terms:
%o prime_factors_with1_reversed(n) = vecsort(setunion([1],factor(n)[,1]~), , 4);
%o partitions_into_with_trailing_ones(n,parts,from=1) = if(!n,1, if(#parts<=(from+1), if(#parts == from,1,(1+(n\parts[from]))), my(s=0); for(i=from,#parts,if(parts[i]<=n, s += partitions_into_with_trailing_ones(n-parts[i],parts,i))); (s)));
%o A014652(n) = partitions_into_with_trailing_ones(n-1,prime_factors_with1_reversed(n)); \\ _Antti Karttunen_, Sep 10 2018
%o (PARI) \\ For an efficient program to compute large numbers of terms, see _David A. Corneth_'s PARI program included in the Links section. - _Antti Karttunen_, Sep 12 2018
%Y Cf. A014648, A014649, A014650, A014651, A066874, A066882, A286852.
%K nonn
%O 1,4
%A _Olivier Gérard_
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