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
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
- David A. Corneth, PARI program
Programs
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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
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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
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