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A359425 Dirichlet convolution of the arithmetic derivative with the primorial base exp-function.

%I A359425 #12 May 14 2025 09:08:56
%S A359425 0,2,2,11,2,19,2,45,18,35,2,85,2,31,40,151,2,125,2,195,36,119,2,313,
%T A359425 38,83,120,215,2,418,2,649,124,491,52,628,2,295,88,1057,2,1046,2,1629,
%U A359425 414,2303,2,1777,38,1541,496,2241,2,4424,140,6421,300,11315,2,2048,2,83,1002,2013,104,1864,2,2073
%N A359425 Dirichlet convolution of the arithmetic derivative with the primorial base exp-function.
%H A359425 Antti Karttunen, <a href="/A359425/b359425.txt">Table of n, a(n) for n = 1..2309</a>
%H A359425 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A359425 a(n) = Sum_{d|n} A003415(n/d) * A276086(d).
%F A359425 a(n) = Sum_{d|n} A347130(n/d) * A383286(d). - _Antti Karttunen_, May 14 2025
%o A359425 (PARI)
%o A359425 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A359425 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A359425 A359425(n) = sumdiv(n,d,A003415(n/d)*A276086(d));
%Y A359425 Cf. A003415, A276086, A359425, A347130, A383286.
%Y A359425 Cf. also A347389, A347959.
%K A359425 nonn,base,look
%O A359425 1,2
%A A359425 _Antti Karttunen_, Jan 02 2023