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Dirichlet convolution of A342001 with A342002.
3

%I #8 Feb 20 2023 07:53:12

%S 0,1,1,3,1,11,1,7,7,15,1,26,1,17,20,19,1,66,1,48,22,55,1,56,9,25,44,

%T 52,1,160,1,47,60,67,26,133,1,33,30,112,1,186,1,140,135,79,1,128,9,86,

%U 72,80,1,256,64,130,38,91,1,372,1,43,155,85,34,406,1,168,84,262,1,241,1,99,127,156,66,472,1,336,130

%N Dirichlet convolution of A342001 with A342002.

%H Antti Karttunen, <a href="/A360121/b360121.txt">Table of n, a(n) for n = 1..11550</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = Sum_{d|n} A342001(n/d) * A342002(d).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A342001(n) = (A003415(n) / A003557(n));

%o A342002(n) = A342001(A276086(n));

%o A360121(n) = sumdiv(n,d,A342001(n/d)*A342002(d));

%Y Cf. A003415, A342001, A342002, A360122 (parity of terms).

%Y Cf. also A347389, A359425.

%K nonn

%O 1,4

%A _Antti Karttunen_, Feb 19 2023