A014652 Number of partitions of n in its prime divisors with at least one part of size 1.

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

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: A069359 A318320 A369741 * A060448 A090080 A151737

Adjacent sequences: A014649 A014650 A014651 * A014653 A014654 A014655

Keyword

nonn

Author

Olivier Gérard

Status

approved