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

%I A328856 #16 Nov 18 2019 02:20:25
%S A328856 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,
%T A328856 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,
%U A328856 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
%N A328856 Number of factorizations of n into distinct numbers with an odd number of distinct prime factors.
%H A328856 Antti Karttunen, <a href="/A328856/b328856.txt">Table of n, a(n) for n = 1..65537</a>
%H A328856 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A328856 Dirichlet g.f.: Product_{k>=1} (1 + A030230(k)^(-s)).
%F A328856 a(n) <= A045778(n). - _Antti Karttunen_, Oct 29 2019
%e A328856 a(32) = 3 because 32 = 4 * 8 = 2 * 16.
%o A328856 (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
%o A328856 (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
%Y A328856 Cf. A030230, A045778, A050332, A328855.
%K A328856 nonn
%O A328856 1,8
%A A328856 _Ilya Gutkovskiy_, Oct 28 2019
%E A328856 More terms from _Antti Karttunen_, Oct 29 2019