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 A228640 a(n) = Sum_{d|n} phi(d)*n^(n/d). 11
 0, 1, 6, 33, 280, 3145, 46956, 823585, 16781472, 387422001, 10000100440, 285311670721, 8916103479504, 302875106592409, 11112006930972780, 437893890382391745, 18446744078004651136, 827240261886336764449, 39346408075494964903956, 1978419655660313589124321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) = Sum_{k=1..n} n^gcd(k,n) = n * A056665(n). - Seiichi Manyama, Mar 10 2021 a(n) = Sum_{k=1..n} n^(n/gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021 MAPLE with(numtheory): a:= n-> add(phi(d)*n^(n/d), d=divisors(n)): seq(a(n), n=0..20); MATHEMATICA a[0] = 0; a[n_] := DivisorSum[n, EulerPhi[#]*n^(n/#)&]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 21 2017 *) PROG (Python) from sympy import totient, divisors def A228640(n):     return sum(totient(d)*n**(n//d) for d in divisors(n, generator=True)) # Chai Wah Wu, Feb 15 2020 (PARI) a(n) = if (n==0, sumdiv(n, d, eulerphi(d)*n^(n/d))); \\ Michel Marcus, Feb 15 2020 (PARI) a(n) = sum(k=1, n, n^gcd(k, n)); \\ Seiichi Manyama, Mar 10 2021 (MAGMA) [0] cat [&+[EulerPhi(d)*n^(n div d): d in Divisors(n)]:n in [1..20]]; // Marius A. Burtea, Feb 15 2020 CROSSREFS Main diagonal of A054618, A054619, A185651. Cf. A000010, A056665. Sequence in context: A215707 A137970 A024079 * A228618 A118094 A343567 Adjacent sequences:  A228637 A228638 A228639 * A228641 A228642 A228643 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 28 2013 STATUS approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)