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A238981 Sum of n-th powers of unitary divisors of n (d such that d divides n, gcd(d, n/d) = 1). 2
1, 5, 28, 257, 3126, 47450, 823544, 16777217, 387420490, 10009766650, 285311670612, 8916117756914, 302875106592254, 11112685048647250, 437893920912786408, 18446744073709551617, 827240261886336764178, 39346558169931834836690, 1978419655660313589123980 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..19.

FORMULA

For prime p, a(p) = p^p + 1; A125137 is a subsequence. - Michel Marcus, Nov 20 2015

a(n) = n^n+1 (A014566) if n is a prime power (A246655). - Michel Marcus, Nov 21 2015

MATHEMATICA

a[n_, k_] := Sum[If[GCD[i, n] == i && GCD[i, n/i] == 1, i^k, 0], {i, n}]; Table[a[n, n], {n, 1, 24}]

PROG

(PARI) a(n) = sumdiv(n, d, d^n*(gcd(d, n/d) == 1)); \\ Michel Marcus, Mar 19 2014

CROSSREFS

Cf. A034448, A238982, A238983.

Sequence in context: A121674 A306181 A116977 * A163694 A062796 A224607

Adjacent sequences:  A238978 A238979 A238980 * A238982 A238983 A238984

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Mar 07 2014

STATUS

approved

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Last modified March 19 11:03 EDT 2019. Contains 321329 sequences. (Running on oeis4.)