cp's OEIS Frontend

A110926 Smaller 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 A110926 #10 Sep 08 2019 04:34:34
%S A110926 6,24,30,40,66,78,102,114,120,120,130,136,138,150,168,174,186,186,215,
%T A110926 222,230,246,258,264,280,280,282,318,330,354,360,366,390,402,408,408,
%U A110926 426,430,438,440,442,456,474,498,510,520,534,552,570,582,600,606,618
%N A110926 Smaller 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 A110926 There do not appear to be any pairs (m,n) such that sigma_k(m)=sigma_k(n) for k>2.
%H A110926 Amiram Eldar, <a href="/A110926/b110926.txt">Table of n, a(n) for n = 1..10000</a>
%F A110926 sigma_2(m)=sigma_2(n), m<n.
%e A110926 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 A110926 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 A110926 Cf. A001157, A002025, A002046, A063990.
%Y A110926 Cf. A110927, A110928, A110929.
%K A110926 nonn
%O A110926 1,1
%A A110926 _Walter Kehowski_, Sep 23 2005