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A344579 a(n) = Sum_{d|n} d^sopf(d). 0

%I

%S 1,5,28,21,3126,7808,823544,85,757,10003130,285311670612,256656,

%T 302875106592254,20661870332,2562893778,341,827240261886336764178,

%U 1898105,1978419655660313589123980,1290003146,16679881801772,282810343194753368,20880467999847912034355032910568,8219344

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

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

%e a(6) = Sum_{d|6} d^sopf(d) = 1^0 + 2^2 + 3^3 + 6^5 = 7808.

%t Table[Sum[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, 30}]

%Y Cf. A008472 (sopf), A344578.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 23 2021

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Last modified May 26 02:08 EDT 2022. Contains 354074 sequences. (Running on oeis4.)