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%I #23 Feb 18 2021 02:42:10
%S 1,2,5,56,59,60,75,122,743,2835,3951,5712,6866,7884,14754,18751,
%T 292123,465289,1921892,3902477,7609760,21855984,22013406
%N Numbers k such that Sum_{i=1..k} sigma(i)^d(i) == 0 (mod k), where sigma = A000203 and d = A000005.
%e sigma(1)^tau(1) + sigma(2)^tau(2) + sigma(3)^tau(3) + sigma(4)^tau(4) + sigma(5)^tau(5) = 1^1 + 3^2 + 4^2 + 7^3 + 6^2 = 1 + 9 + 16 + 343 + 36 = 405 and 405 / 5 = 81.
%p with(numtheory): P:=proc(q) local a,n; a:=0;
%p for n from 1 to q do a:=a+sigma(n)^tau(n);
%p if a mod n=0 then print(n); fi; od; end: P(10^6);
%o (PARI) for(n=1, 1e4, if(sum(k=1, n, sigma(k)^numdiv(k))%n==0, print1(n", "))) \\ _Altug Alkan_, Nov 13 2015
%Y Cf. A000005, A000203, A227427, A227429, A227502, A227848, A229095, A229207, A229208, A229209, A229210, A229211.
%K nonn,more
%O 1,2
%A _Paolo P. Lava_, Nov 13 2015
%E Incorrect terms removed by and more terms from _Jinyuan Wang_, Feb 18 2021
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