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A014652 Number of partitions of n in its prime divisors with at least one part of size 1. 6
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, 226, 1, 16, 23, 26, 23, 120, 1, 29, 27, 92, 1, 422, 1, 56, 78, 35, 1, 208, 7, 140, 35, 66, 1, 261, 35, 128, 39, 44, 1, 1487, 1, 47, 108, 32, 41, 996, 1, 86, 47, 1062, 1, 456, 1, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

David A. Corneth, PARI program

FORMULA

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

PROG

(PARI)

\\ This is for computing just a moderate number of terms:

prime_factors_with1_reversed(n) = vecsort(setunion([1], factor(n)[, 1]~), , 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)));

A014652(n) = partitions_into_with_trailing_ones(n-1, prime_factors_with1_reversed(n)); \\ Antti Karttunen, Sep 10 2018

(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

CROSSREFS

Cf. A014648, A014649, A014650, A014651, A066874, A066882, A286852.

Sequence in context: A205443 A069359 A318320 * A060448 A090080 A151737

Adjacent sequences:  A014649 A014650 A014651 * A014653 A014654 A014655

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)