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A328856
Number of factorizations of n into distinct numbers with an odd number of distinct prime factors.
2
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 28 2019
EXTENSIONS
More terms from Antti Karttunen, Oct 29 2019
STATUS
approved