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%I #13 Feb 08 2020 11:57:49
%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,2,1,1,1,6,1,1,1,2,1,15,1,1,1,1,
%T 1,16,1,1,1,6,1,21,1,2,3,1,1,26,1,5,1,2,1,18,1,6,1,1,1,238,1,1,3,1,1,
%U 31,1,2,1,31,1,139,1,1,5,2,1,37,1,26,1,1,1,414,1,1,1,6,1,612,1,2,1,1
%N Number of partitions of n into its nonprime power divisors with at least one part of size 1.
%H Antti Karttunen, <a href="/A014649/b014649.txt">Table of n, a(n) for n = 1..20000</a>
%H David A. Corneth & Antti Karttunen, <a href="/A014649/a014649.txt">PARI program</a>
%o (PARI)
%o \\ This is for computing a small number of terms:
%o nonprimepower_divisors_with1_reversed(n) = vecsort(select(d -> ((1==d) || !isprimepower(d)), divisors(n)), , 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 A014649(n) = partitions_into_with_trailing_ones(n-1, nonprimepower_divisors_with1_reversed(n)); \\ _Antti Karttunen_, Aug 23 2019
%o (PARI) \\ For an efficient program to compute large numbers of terms, see PARI program included in the Links-section.
%Y Cf. A014648, A014650, A014651, A014652, A066874.
%K nonn
%O 1,12
%A _Olivier Gérard_
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