cp's OEIS Frontend

A110927 Larger of the pair of distinct numbers m and n such that sigma_2(m)=sigma_2(n), where sigma_2(n) is the sum of the squares of all divisors of n.

%I A110927 #10 Sep 08 2019 04:34:30
%S A110927 7,26,35,47,77,91,119,133,130,141,141,157,161,175,182,203,215,217,217,
%T A110927 259,249,287,301,286,282,329,329,371,385,413,423,427,455,469,442,471,
%U A110927 497,434,511,517,471,494,553,581,595,611,623,598,665,679,650,707,721
%N A110927 Larger of the pair of distinct numbers m and n such that sigma_2(m)=sigma_2(n), where sigma_2(n) is the sum of the squares of all divisors of n.
%C A110927 There do not appear to be any pairs (m,n) such that sigma_k(m)=sigma_k(n) for k>2.
%H A110927 Amiram Eldar, <a href="/A110927/b110927.txt">Table of n, a(n) for n = 1..10000</a>
%F A110927 sigma_2(m)=sigma_2(n), m<n.
%e A110927 sigma_2(30)=1^1+2^2+3^2+5^2+6^2+10^2+15^2+30^2=1300 and sigma_2(35)=1^2+5^2+7^2+35^2=1300.
%p A110927 with(numtheory); sigmap := proc(p,n) convert(map(proc(z) z^p end, divisors(n)),`+`) end; SA2:=[]: for z from 1 to 1 do for m to 1500 do M:=sigmap(2,m); for n from m+1 to 1500 do N:=sigmap(2,n); if N=M then SA2:=[op(SA2),[m,n,N]] fi od od od; SA2; select(proc(z) z[1]<=1000 end, SA2); #just to shorten it a bit
%Y A110927 Cf. A001157, A002025, A002046, A063990.
%Y A110927 Cf. A110926, A110928, A110929.
%K A110927 nonn
%O A110927 1,1
%A A110927 _Walter Kehowski_, Sep 23 2005