A131905 Integers x such that sigma_2(k)=sigma_2(x) for some 0A001157=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

Author

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

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A069822, A131902-A131908.

Programs

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 *)

PARI

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

Formula

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

Extensions

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

Edited by Danny Rorabaugh, Apr 03 2015