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A228640
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a(n) = Sum_{d|n} phi(d)*n^(n/d).
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10
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0, 1, 6, 33, 280, 3145, 46956, 823585, 16781472, 387422001, 10000100440, 285311670721, 8916103479504, 302875106592409, 11112006930972780, 437893890382391745, 18446744078004651136, 827240261886336764449, 39346408075494964903956, 1978419655660313589124321
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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a(n) = Sum_{k=1..n} n^gcd(k,n) = n * A056665(n). - Seiichi Manyama, Mar 10 2021
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MAPLE
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with(numtheory):
a:= n-> add(phi(d)*n^(n/d), d=divisors(n)):
seq(a(n), n=0..20);
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MATHEMATICA
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a[0] = 0; a[n_] := DivisorSum[n, EulerPhi[#]*n^(n/#)&]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 21 2017 *)
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PROG
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(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
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CROSSREFS
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Main diagonal of A054618, A054619, A185651.
Cf. A000010, A056665.
Sequence in context: A215707 A137970 A024079 * A228618 A118094 A306182
Adjacent sequences: A228637 A228638 A228639 * A228641 A228642 A228643
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Aug 28 2013
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STATUS
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approved
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