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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..11550

Index entries for sequences related to primorial base

Formula

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

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

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 *)

Prog

(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));

Crossrefs

Cf. A000010, A324198.

Cf. also A346242, A347131, A347235, A347958.

Sequence in context: A276320 A011036 A086267 * A197288 A053424 A184617

Adjacent sequences: A348024 A348025 A348026 * A348028 A348029 A348030

Keyword

nonn,base

Author

Antti Karttunen, Sep 25 2021

Status

approved