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%I #14 Nov 27 2021 11:03:59
%S 1,2,5,4,5,8,7,8,15,14,11,16,13,14,37,16,17,24,19,28,35,22,23,32,49,
%T 26,45,28,29,60,31,32,55,34,41,48,37,38,65,56,41,62,43,44,111,46,47,
%U 64,55,114,85,52,53,72,59,62,95,58,59,120,61,62,123,64,65,88,67,68,115,134,71,96,73,74,293,76,83,104,79
%N Dirichlet convolution of Euler phi with A324198.
%H Antti Karttunen, <a href="/A348027/b348027.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} phi(n/d) * A324198(d).
%F a(n) = Sum_{k=1..n} A324198(gcd(n,k)).
%t s[n_] := Module[{k = n, m = 1, p = 2}, While[k > 0, m *= (p^Min[Mod[k, p], IntegerExponent[n, p]]); k = Quotient[k, p]; p = NextPrime[p]]; m]; a[n_] := DivisorSum[n, s[#] * EulerPhi[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 27 2021 *)
%o (PARI)
%o A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
%o A348027(n) = sumdiv(n,d,eulerphi(d)*A324198(n/d));
%Y Cf. A000010, A324198.
%Y Cf. also A346242, A347131, A347235, A347958.
%K nonn,base
%O 1,2
%A _Antti Karttunen_, Sep 25 2021
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