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A348027
Dirichlet convolution of Euler phi with A324198.
1
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
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
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Sep 25 2021
STATUS
approved