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.
6, 24, 30, 40, 66, 78, 102, 114, 120, 120, 130, 136, 138, 150, 168, 174, 186, 186, 215, 222, 230, 246, 258, 264, 280, 280, 282, 318, 330, 354, 360, 366, 390, 402, 408, 408, 426, 430, 438, 440, 442, 456, 474, 498, 510, 520, 534, 552, 570, 582, 600, 606, 618
Offset: 1
Keywords
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
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
Formula
sigma_2(m)=sigma_2(n), m
Comments