A332621
a(n) = (1/n) * Sum_{k=1..n} n^(n/gcd(n, k)).
Original entry on oeis.org
1, 3, 19, 133, 2501, 15631, 705895, 8389641, 258280489, 4000040011, 259374246011, 2972033984173, 279577021469773, 4762288684702095, 233543408203327951, 9223372037928525841, 778579070010669895697, 13115469358498302735067, 1874292305362402347591139
Offset: 1
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[(1/n)*&+[n^(n div Gcd(n,k)):k in [1..n]]:n in [1..20]]; // Marius A. Burtea, Feb 17 2020
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Table[(1/n) Sum[n^(n/GCD[n, k]), {k, 1, n}], {n, 1, 19}]
Table[(1/n) Sum[EulerPhi[d] n^d, {d, Divisors[n]}], {n, 1, 19}]
Table[SeriesCoefficient[Sum[Sum[EulerPhi[j] n^(j - 1) x^(k j), {j, 1, n}], {k, 1, n}], {x, 0, n}], {n, 1, 19}]
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a(n) = sum(k=1, n, n^(n/gcd(n, k)))/n; \\ Michel Marcus, Mar 10 2021
A332653
a(n) = (1/n) * Sum_{k=1..n} n^(k/gcd(n, k)).
Original entry on oeis.org
1, 2, 5, 19, 157, 1306, 19609, 266372, 5321721, 101001214, 2593742461, 61920391842, 1941507093541, 56984643437138, 2076518238897649, 72340172854919941, 3041324492229179281, 121440691499123469858, 5784852794328402307381, 262799364106291328009626
Offset: 1
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[(1/n)*&+[n^(k div Gcd(n,k)):k in [1..n]]:n in [1..21]]; // Marius A. Burtea, Feb 18 2020
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Table[(1/n) Sum[n^(k/GCD[n, k]), {k, 1, n}], {n, 1, 20}]
Table[Sum[Sum[If[GCD[k, d] == 1, n^(k - 1), 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 20}]
A332652
a(n) = Sum_{k=1..n} n^(k/gcd(n, k)).
Original entry on oeis.org
1, 4, 15, 76, 785, 7836, 137263, 2130976, 47895489, 1010012140, 28531167071, 743044702104, 25239592216033, 797785008119932, 31147773583464735, 1157442765678719056, 51702516367896047777, 2185932446984222457444, 109912203092239643840239, 5255987282125826560192520
Offset: 1
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[&+[n^(k div Gcd(n,k)):k in [1..n]]:n in [1..21]]; // Marius A. Burtea, Feb 18 2020
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Table[Sum[n^(k/GCD[n, k]), {k, 1, n}], {n, 1, 20}]
Table[Sum[Sum[If[GCD[k, d] == 1, n^k, 0], {k, 1, d}], {d, Divisors[n]}], {n, 1, 20}]
A342395
a(n) = Sum_{k=1..n} k^(n/gcd(k,n)).
Original entry on oeis.org
1, 3, 12, 90, 1305, 15713, 376768, 6163324, 176787369, 3769360335, 142364319636, 3152514811878, 154718778284161, 4340009168261557, 210971169749009040, 7281661102087491416, 435659030617933827153, 14181101408651996188995
Offset: 1
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a[n_] := Sum[k^(n/GCD[k, n]), {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Mar 10 2021 *)
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a(n) = sum(k=1, n, k^(n/gcd(k, n)));
Showing 1-4 of 4 results.