A110927 Larger 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.
7, 26, 35, 47, 77, 91, 119, 133, 130, 141, 141, 157, 161, 175, 182, 203, 215, 217, 217, 259, 249, 287, 301, 286, 282, 329, 329, 371, 385, 413, 423, 427, 455, 469, 442, 471, 497, 434, 511, 517, 471, 494, 553, 581, 595, 611, 623, 598, 665, 679, 650, 707, 721
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
A110928
Pairs of distinct numbers m and n, m
6, 7, 24, 26, 30, 35, 40, 47, 66, 77, 78, 91, 102, 119, 114, 133, 120, 130, 120, 141, 130, 141, 136, 157, 138, 161, 150, 175, 168, 182, 174, 203, 186, 215, 186, 217, 215, 217, 222, 259, 230, 249, 246, 287, 258, 301, 264, 286, 280, 282, 280, 329, 282, 329, 318
Offset: 1
Comments
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
-
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, k]], {k, n + 1, kmax}]; ans]; s = {}; Do[v = a[n]; Do[s = Join[s, {n, v[[k]]}], {k, 1, Length[v]}], {n, 1, 400}]; s (* Amiram Eldar, Sep 08 2019 *)
Formula
sigma_2(m)=sigma_2(n), m
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
-
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
Comments