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%I #17 Feb 08 2020 11:57:25
%S 1,1,1,2,1,5,1,6,3,8,1,27,1,11,11,26,1,43,1,63,15,17,1,215,5,20,18,
%T 114,1,226,1,166,23,26,23,734,1,29,27,728,1,422,1,261,181,35,1,2697,7,
%U 179,35,357,1,791,35,1729,39,44,1,6747,1,47,325,1626,41,996,1,594,47,1062,1,20345,1,56,327,735,47,1374,1,13485,216,62,1
%N Number of partitions of n into its divisors that are powers of primes (A000961) with at least one part of size 1.
%H Antti Karttunen, <a href="/A014650/b014650.txt">Table of n, a(n) for n = 1..10000</a>
%H David A. Corneth, <a href="/A014650/a014650.txt">PARI program</a>
%o (PARI)
%o \\ This is for computing a small number of terms:
%o primepower_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 A014650(n) = partitions_into_with_trailing_ones(n-1,primepower_divisors_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. A000961, A014648, A014649, A014651, A014652, A066874.
%K nonn
%O 1,4
%A _Olivier Gérard_
%E More terms from and the name clarified by _Antti Karttunen_, Sep 10 2018
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