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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.
4

%I #10 Sep 08 2019 04:34:34

%S 6,24,30,40,66,78,102,114,120,120,130,136,138,150,168,174,186,186,215,

%T 222,230,246,258,264,280,280,282,318,330,354,360,366,390,402,408,408,

%U 426,430,438,440,442,456,474,498,510,520,534,552,570,582,600,606,618

%N 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 There do not appear to be any pairs (m,n) such that sigma_k(m)=sigma_k(n) for k>2.

%H Amiram Eldar, <a href="/A110926/b110926.txt">Table of n, a(n) for n = 1..10000</a>

%F sigma_2(m)=sigma_2(n), m<n.

%e 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 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 Cf. A001157, A002025, A002046, A063990.

%Y Cf. A110927, A110928, A110929.

%K nonn

%O 1,1

%A _Walter Kehowski_, Sep 23 2005