A328856 Number of factorizations of n into distinct numbers with an odd number of distinct prime factors.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 2

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

Formula

Dirichlet g.f.: Product_{k>=1} (1 + A030230(k)^(-s)).

a(n) <= A045778(n). - Antti Karttunen, Oct 29 2019

Example

a(32) = 3 because 32 = 4 * 8 = 2 * 16.

Prog

(PARI) seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, if(omega(k)%2, my(m=logint(n, k), p=(1 + x + O(x*x^m)), w=vector(n)); for(i=0, m, w[k^i]=polcoef(p, i)); v=dirmul(v, w))); v} \\ Andrew Howroyd, Oct 29 2019, In older versions of PARI, use polcoeff instead of polcoef. - Antti Karttunen, Oct 29 2019
(PARI) A328856(n, k=n) = (((n<=k)&&((1==n)||(omega(n)%2))) + sumdiv(n, d, if(d > 1 && d <= k && d < n && (omega(d)%2), A328856(n/d, d-1)))); \\ Antti Karttunen, Oct 29 2019

Crossrefs

Cf. A030230, A045778, A050332, A328855.

Sequence in context: A050361 A072911 A325988 * A053150 A295657 A163379

Adjacent sequences: A328853 A328854 A328855 * A328857 A328858 A328859

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 28 2019

Extensions

More terms from Antti Karttunen, Oct 29 2019

Status

approved