A110929
The common value of sigma_2 for square-amicable numbers, sigma_2(m)=sigma_2(n), m
50, 850, 1300, 2210, 6100, 8500, 14500, 18100, 22100, 22100, 22100, 24650, 26500, 32550, 42500, 42100, 48100, 48100, 48100, 68500, 68900, 84100, 92500, 103700, 110500, 110500, 110500, 140500, 158600, 174100, 201110, 186100, 221000, 224500
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
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Mathematica
a[n_] := Module[{s = DivisorSigma[2, n], ans = {}}, kmax = Ceiling[Sqrt[s]]; Do[If[DivisorSigma[2, k] == s, AppendTo[ans, s]], {k, n + 1, kmax}]; ans]; s = {}; Do[v = a[n]; Do[AppendTo[s, v[[k]]], {k, 1, Length[v]}], {n, 1, 400}]; s (* Amiram Eldar, Sep 08 2019 *)
Formula
sigma_2(m)=sigma_2(n), m