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A348397 a(n) = Sum_{d|n} sigma_[n-d](d), where sigma_[k](n) is the sum of the k-th powers of the divisors of n.

%I A348397 #19 Dec 10 2021 11:19:57
%S A348397 1,3,3,9,3,50,3,343,734,3388,3,133959,3,827646,10297073,33640713,3,
%T A348397 2579172499,3,44822639761,678610493345,285312719194,3,393067887861756,
%U A348397 95367431640630,302875123369476,150094918113956098,569940024192528003,3,105474401758856279784,3
%N A348397 a(n) = Sum_{d|n} sigma_[n-d](d), where sigma_[k](n) is the sum of the k-th powers of the divisors of n.
%H A348397 Michel Marcus, <a href="/A348397/b348397.txt">Table of n, a(n) for n = 1..500</a>
%F A348397 a(n) = 3 iff n is prime. - _Bernard Schott_, Oct 17 2021
%e A348397 a(6) = 50; a(6) = sigma_[6-1](1) + sigma_[6-2](2) + sigma_[6-3](3) + sigma_[6-6](6) = (1^5) + (1^4 + 2^4) + (1^3 + 3^3) + (6^0 + 6^0 + 6^0 + 6^0) = 50.
%t A348397 a[n_] := DivisorSum[n, DivisorSigma[n - #, #] &]; Array[a, 30] (* _Amiram Eldar_, Oct 17 2021 *)
%o A348397 (PARI) a(n) = sumdiv(n, d, sigma(d, n-d)); \\ _Michel Marcus_, Oct 18 2021
%Y A348397 Cf. A321141.
%K A348397 nonn
%O A348397 1,2
%A A348397 _Wesley Ivan Hurt_, Oct 16 2021