A349542 Number of partitions of n into distinct unitary divisors of n.
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
Offset: 0
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 0..20000
Programs
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Mathematica
a[n_] := SeriesCoefficient[Product[(1 + Boole[GCD[n/d, d] == 1] x^d), {d, Divisors[n]}], {x, 0, n}]; Table[a[n], {n, 0, 114}] -
PARI
A349542(n) = if(!n, 1, my(p=1); fordiv(n,d, if(1==gcd(d,n/d), p *= (1 + 'x^d))); polcoeff(p,n)); \\ Antti Karttunen, Nov 22 2021
Formula
a(n) = [x^n] Product_{d|n, gcd(d,n/d) = 1} (1 + x^d).