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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).

%I A238981 #38 Apr 28 2023 16:40:28
%S A238981 1,5,28,257,3126,47450,823544,16777217,387420490,10009766650,
%T A238981 285311670612,8916117756914,302875106592254,11112685048647250,
%U A238981 437893920912786408,18446744073709551617,827240261886336764178,39346558169931834836690,1978419655660313589123980
%N A238981 Sum of n-th powers of unitary divisors of n (d such that d divides n, gcd(d, n/d) = 1).
%H A238981 Amiram Eldar, <a href="/A238981/b238981.txt">Table of n, a(n) for n = 1..387</a>
%F A238981 For prime p, a(p) = p^p + 1; A125137 is a subsequence. - _Michel Marcus_, Nov 20 2015
%F A238981 a(n) = n^n+1 (A014566) if n is a prime power (A246655). - _Michel Marcus_, Nov 21 2015
%F A238981 a(n) = Sum_{d|n, gcd(d,n/d)=1} d^n. - _Wesley Ivan Hurt_, Apr 28 2023
%t A238981 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}]
%t A238981 a[1] = 1; a[n_] := Times @@ (1 + First[#]^(n * Last[#]) &/@ FactorInteger[n]);  Array[a, 19] (* _Amiram Eldar_, Aug 10 2019 *)
%o A238981 (PARI) a(n) = sumdiv(n, d, d^n*(gcd(d, n/d) == 1)); \\ _Michel Marcus_, Mar 19 2014
%Y A238981 Cf. A034448, A238982, A238983.
%K A238981 nonn
%O A238981 1,2
%A A238981 _José María Grau Ribas_, Mar 07 2014