cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A345274 a(n) = Sum_{d|n} (n-d)^tau(n/d).

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%I A345274 #3 Jun 12 2021 20:33:06
%S A345274 0,1,4,31,16,650,36,2633,548,6650,100,1782390,144,28754,38660,799583,
%T A345274 256,24192515,324,47154588,160520,195002,484,78424725898,14224,391370,
%U A345274 471124,387887498,784,500247950884,900,912432417,1049960,1187234,1338020,78818475807611,1296,1875818
%N A345274 a(n) = Sum_{d|n} (n-d)^tau(n/d).
%C A345274 If p is prime, a(p) = Sum_{d|p} (p-d)^tau(p/d) = (p-1)^2 + 0^1 = (p-1)^2.
%e A345274 a(10) = Sum_{d|10} (10-d)^tau(10/d) = 9^4 + 8^2 + 5^2 + 0^1 = 6650.
%t A345274 Table[Sum[(n - k)^DivisorSigma[0, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]
%Y A345274 Cf. A000005 (tau), A174937.
%K A345274 nonn
%O A345274 1,3
%A A345274 _Wesley Ivan Hurt_, Jun 12 2021