cp's OEIS Frontend

A260654 Numbers k such that Sum_{i=1..k} sigma(i)^d(i) == 0 (mod k), where sigma = A000203 and d = A000005.

%I A260654 #28 Dec 29 2024 03:43:46
%S A260654 1,2,5,56,59,60,75,122,743,2835,3951,5712,6866,7884,14754,18751,
%T A260654 292123,465289,1921892,3902477,7609760,21855984,22013406,358753359,
%U A260654 570535294,582046711,1846338478,13691385818
%N A260654 Numbers k such that Sum_{i=1..k} sigma(i)^d(i) == 0 (mod k), where sigma = A000203 and d = A000005.
%e A260654 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 A260654 with(numtheory): P:=proc(q) local a,n; a:=0;
%p A260654 for n from 1 to q do a:=a+sigma(n)^tau(n);
%p A260654 if a mod n=0 then print(n); fi; od; end: P(10^6);
%o A260654 (PARI) for(n=1, 1e4, if(sum(k=1, n, sigma(k)^numdiv(k))%n==0, print1(n", "))) \\ _Altug Alkan_, Nov 13 2015
%o A260654 (PARI) list(lim) = {my(s = 0, f); for(k = 1, lim, f = factor(k); s += sigma(f)^numdiv(f); if(!(s % k), print1(k, ", ")));} \\ _Amiram Eldar_, Dec 29 2024
%Y A260654 Cf. A000005, A000203, A227427, A227429, A227502, A227848, A229095, A229207, A229208, A229209, A229210, A229211.
%K A260654 nonn,more
%O A260654 1,2
%A A260654 _Paolo P. Lava_, Nov 13 2015
%E A260654 Incorrect terms removed by and more terms from _Jinyuan Wang_, Feb 18 2021
%E A260654 a(24)-a(28) from _Amiram Eldar_, Dec 29 2024