A014649 - OEIS

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A014649

Number of partitions of n into its nonprime power divisors with at least one part of size 1.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,12

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

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

Cf. A014648, A014650, A014651, A014652, A066874.

Sequence in context: A062760 A323163 A322318 * A326568 A279817 A309386

Adjacent sequences: A014646 A014647 A014648 * A014650 A014651 A014652

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved