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

%I A131905 #18 May 22 2024 17:21:31
%S A131905 7,26,35,47,77,91,119,130,133,141,157,161,175,182,203,215,217,249,259,
%T A131905 282,286,287,301,329,371,385,413,423,427,434,442,455,469,471,494,497,
%U A131905 511,517,553,581,595,598,611,623,650,651,665,679,707,721,749,754,763,785
%N 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.
%H A131905 Robert Israel, <a href="/A131905/b131905.txt">Table of n, a(n) for n = 1..10000</a>
%F A131905 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.
%e A131905 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.
%p A131905 N:= 100: # to get a(1)..a(N)
%p A131905 count:= 0: Res:= NULL:
%p A131905 for n from 1 while count < N do
%p A131905   v:= numtheory:-sigma[2](n);
%p A131905   if assigned(V[v]) then count:= count+1; Res:= Res, n;
%p A131905   else V[v]:= n
%p A131905   fi
%p A131905 od:
%p A131905 Res; # _Robert Israel_, Mar 30 2018
%t A131905 Clear[tmp]; First@Transpose[ Function[n, (If[Head[ #1] === tmp, #1 = n; Unevaluated[Sequence[]], {n, #1}] & )[tmp[DivisorSigma[2, n]]]] /@ Range[500]]
%t A131905 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 *)
%o A131905 (PARI) isok(n) = {sn = sigma(n,2); for (k=1, n-1, if (sigma(k,2) == sn, return (1)););} \\ _Michel Marcus_, Apr 03 2015
%Y A131905 Cf. A069822, A131902-A131908.
%K A131905 easy,nonn
%O A131905 1,1
%A A131905 Peter Pein (petsie(AT)dordos.net), Jul 26 2007
%E A131905 a(37)-a(54) from _Michel Marcus_, Apr 03 2015
%E A131905 Edited by _Danny Rorabaugh_, Apr 03 2015