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a(n) = Sum_{d|n} n^sigma(d).
3

%I #15 Oct 08 2021 12:15:20

%S 1,10,84,16452,15630,2176783854,5764808,35184374186504,2541865834899,

%T 1000000000001001010,3138428376732,1648446623609512552867179993036,

%U 3937376385699302,3214199700417740938226879430,16834112196028232574474331890,21267647932558653967613834469360799760

%N a(n) = Sum_{d|n} n^sigma(d).

%H Seiichi Manyama, <a href="/A345895/b345895.txt">Table of n, a(n) for n = 1..167</a>

%F a(prime(n)) = A104128(n). - _Michel Marcus_, Jun 29 2021

%e a(4) = Sum_{d|4} 4^sigma(d) = 4^1 + 4^3 + 4^7 = 16452.

%t a[n_] := DivisorSum[n, n^DivisorSigma[1, #] &]; Array[a, 16] (* _Amiram Eldar_, Jun 29 2021 *)

%o (PARI) a(n) = sumdiv(n, d, n^sigma(d)); \\ _Michel Marcus_, Jun 29 2021

%Y Cf. A000203 (sigma), A104128, A174472, A345271.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 28 2021