A110929 The common value of sigma_2 for square-amicable numbers, sigma_2(m)=sigma_2(n), m<n.

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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

Example

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.

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

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 *)

Crossrefs

Cf. A001157, A002025, A002046, A063990.

Cf. A110926, A110927, A110928.

Sequence in context: A160287 A104672 A086027 * A329713 A101929 A006360

Adjacent sequences: A110926 A110927 A110928 * A110930 A110931 A110932

Keyword

nonn

Author

Walter Kehowski, Sep 23 2005

Status

approved