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 A343274 a(n) = Sum_{d|n} d^d * sopf(d). 0

%I

%S 0,8,81,520,15625,233369,5764801,33554952,1162261548,70000015633,

%T 3138428376721,44580502475161,3937376385699289,100008061435786953,

%U 3503151123046890706,36893488147452658184,14063084452067724991009,196732040376483850371956,37589973457545958193355601

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

%C If p is prime, a(p) = Sum_{d|p} d^d * sopf(d) = 1^1*0 + p^p*p = p^(p+1).

%e a(4) = Sum_{d|4} d^d * sopf(d) = 1^1*sopf(1) + 2^2*sopf(2) + 4^4*sopf(4) = 0 + 8 + 512 = 520.

%t Table[Sum[i^i*Sum[k (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k]), {k, i}] (1 - Ceiling[n/i] + Floor[n/i]) , {i, n}], {n, 20}]

%Y Cf. A008472 (sopf).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 24 2021

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Last modified November 27 13:54 EST 2022. Contains 358405 sequences. (Running on oeis4.)