A131905 Integers x such that sigma_2(k)=sigma_2(x) for some 0<k<x, where A001157=sigma_2 is the sum of squares of divisors.

7, 26, 35, 47, 77, 91, 119, 130, 133, 141, 157, 161, 175, 182, 203, 215, 217, 249, 259, 282, 286, 287, 301, 329, 371, 385, 413, 423, 427, 434, 442, 455, 469, 471, 494, 497, 511, 517, 553, 581, 595, 598, 611, 623, 650, 651, 665, 679, 707, 721, 749, 754, 763, 785

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = n-th element of {x: there exists some k with 0<k<x and sigma_2(m)=sigma_2(n)}, where A001157=sigma_2 is the sum of squares of divisors.

Example

This sequence contains 35, because sigma_2(35) = 1^2+5^2+7^2+35^2 = 1+25+49+1225 = 1300, and the sum of the squares of the divisors of 30<35 is sigma_2(30) = 1+4+9+25+36+100+225+900 = 1300.

Maple

N:= 100: # to get a(1)..a(N)
count:= 0: Res:= NULL:
for n from 1 while count < N do
  v:= numtheory:-sigma[2](n);
  if assigned(V[v]) then count:= count+1; Res:= Res, n;
  else V[v]:= n
  fi
od:
Res; # Robert Israel, Mar 30 2018

Mathematica

Clear[tmp]; First@Transpose[ Function[n, (If[Head[ #1] === tmp, #1 = n; Unevaluated[Sequence[]], {n, #1}] & )[tmp[DivisorSigma[2, n]]]] /@ Range[500]]
Module[{nn=800, ds2, c}, ds2=DivisorSigma[2, Range[nn]]; Table[c=TakeDrop[Take[ds2, n], -1]; If[ MemberQ[c[[2]], c[[1, 1]]], n, Nothing], {n, nn}]] (* Harvey P. Dale, May 22 2024 *)

Prog

(PARI) isok(n) = {sn = sigma(n, 2); for (k=1, n-1, if (sigma(k, 2) == sn, return (1)); ); } \\ Michel Marcus, Apr 03 2015

Crossrefs

Cf. A069822, A131902-A131908.

Sequence in context: A246910 A098127 A283427 * A110927 A103267 A125972

Adjacent sequences: A131902 A131903 A131904 * A131906 A131907 A131908

Keyword

easy,nonn

Author

Peter Pein (petsie(AT)dordos.net), Jul 26 2007

Extensions

a(37)-a(54) from Michel Marcus, Apr 03 2015

Edited by Danny Rorabaugh, Apr 03 2015

Status

approved