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A014649
Number of partitions of n into its nonprime power divisors with at least one part of size 1.
3
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, 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, 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
OFFSET
1,12
LINKS
David A. Corneth & Antti Karttunen, PARI program
PROG
(PARI)
\\ This is for computing a small number of terms:
nonprimepower_divisors_with1_reversed(n) = vecsort(select(d -> ((1==d) || !isprimepower(d)), divisors(n)), , 4);
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)));
A014649(n) = partitions_into_with_trailing_ones(n-1, nonprimepower_divisors_with1_reversed(n)); \\ Antti Karttunen, Aug 23 2019
(PARI) \\ For an efficient program to compute large numbers of terms, see PARI program included in the Links-section.
CROSSREFS
KEYWORD
nonn
STATUS
approved