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A378755 Dirichlet convolution of A033879 and A346248.

%I A378755 #6 Dec 11 2024 20:18:03
%S A378755 1,0,1,2,1,2,3,10,11,2,1,14,3,6,7,42,1,26,3,14,17,2,5,70,15,6,81,34,1,
%T A378755 22,5,170,7,2,17,146,3,6,17,70,1,54,3,14,69,10,5,326,55,34,7,34,5,234,
%U A378755 7,162,17,2,1,138,5,10,155,682,17,22,3,14,27,54,1,730,5,6,89,34,17,54,3,326,571,2,5,318,7,6,7
%N A378755 Dirichlet convolution of A033879 and A346248.
%H A378755 Antti Karttunen, <a href="/A378755/b378755.txt">Table of n, a(n) for n = 1..20000</a>
%H A378755 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A378755 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A378755 a(n) = Sum_{d|n} A033879(d)*A346248(n/d).
%o A378755 (PARI)
%o A378755 A033879(n) = (n+n-sigma(n));
%o A378755 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378755 A252748(n) = (A003961(n) - (2*n));
%o A378755 memoA346248 = Map();
%o A378755 A346248(n) = if(1==n,1,my(v); if(mapisdefined(memoA346248,n,&v), v, v = -sumdiv(n,d,if(d<n,-A252748(n/d)*A346248(d),0)); mapput(memoA346248,n,v); (v)));
%o A378755 A378755(n) = sumdiv(n,d,A033879(d)*A346248(n/d));
%Y A378755 Cf. A033879, A346248, A378754 (Dirichlet inverse).
%K A378755 nonn
%O A378755 1,4
%A A378755 _Antti Karttunen_, Dec 11 2024