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A329373 Dirichlet convolution of the identity function with A322993.

%I A329373 #12 Nov 12 2019 19:20:53
%S A329373 0,1,1,5,1,10,1,17,6,16,1,40,1,26,13,49,1,49,1,66,19,46,1,124,8,80,25,
%T A329373 108,1,114,1,129,31,148,17,185,1,278,49,206,1,182,1,192,65,538,1,340,
%U A329373 10,111,85,330,1,190,25,336,151,1056,1,428,1,2082,97,321,35,318,1,606,283,258,1,557,1,4136,87,1128,23,530,1,566,90,8236,1,684,55,16430
%N A329373 Dirichlet convolution of the identity function with A322993.
%C A329373 Equally, Dirichlet convolution of sigma (A000203) with A322994 (Möbius transform of A322993).
%H A329373 Antti Karttunen, <a href="/A329373/b329373.txt">Table of n, a(n) for n = 1..2001</a>
%H A329373 Antti Karttunen, <a href="/A329373/a329373.txt">Data supplement: n, a(n) computed for n = 1..32768</a>
%H A329373 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A329373 a(n) = Sum_{d|n} d * A322993(n/d).
%F A329373 a(n) = Sum_{d|n} A000203(n/d) * A322994(d).
%o A329373 (PARI)
%o A329373 A000265(n) = (n/2^valuation(n, 2));
%o A329373 A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A329373 A322993(n) = if(1==n,0,A000265(A156552(n)));
%o A329373 A329373(n) = sumdiv(n,d,(n/d)*A322993(d));
%Y A329373 Cf. A000203, A000265, A156552, A322993, A322994, A324542, A329372, A329374.
%K A329373 nonn
%O A329373 1,4
%A A329373 _Antti Karttunen_, Nov 12 2019