A348027 Dirichlet convolution of Euler phi with A324198.

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, 26, 45, 28, 29, 60, 31, 32, 55, 34, 41, 48, 37, 38, 65, 56, 41, 62, 43, 44, 111, 46, 47, 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

Offset: 1

Author

Antti Karttunen, Sep 25 2021

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A000010, A324198.

Cf. also A346242, A347131, A347235, A347958.

Programs

Mathematica

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 *)

PARI

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); };
A348027(n) = sumdiv(n,d,eulerphi(d)*A324198(n/d));

Formula

a(n) = Sum_{d|n} phi(n/d) * A324198(d).

a(n) = Sum_{k=1..n} A324198(gcd(n,k)).