|
%I #24 Aug 31 2020 14:58:00
%S 61,2369,4469,8460,13208,44790,162734,281560,283938,334469,500465,
%T 533045,609953,871853,962247,1317885,1741445,1792745,2499845,3013246,
%U 4099031,5646629,7009389,7012135,8396781,8740480,8822093,11146381,11957693,15002679,18895694
%N Numbers n such that sigma(n)+d(n) and sigma(n+1)+d(n+1) are perfect squares.
%H Amiram Eldar, <a href="/A224441/b224441.txt">Table of n, a(n) for n = 1..100</a>
%e 61 is in the list since sigma(61)+d(61)=64 and sigma(62)+d(62)=100.
%t Sqd[n_] := Sqrt[DivisorSigma[1, n] + DivisorSigma[0, n]]; t = {}; Do[If[IntegerQ[Sqd[n]] && IntegerQ[Sqd[n + 1]], AppendTo[t, n]], {n, 20000000}]; t
%t SequencePosition[Table[If[IntegerQ[Sqrt[DivisorSigma[0,n]+DivisorSigma[1,n]]],1,0],{n,189*10^5}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 31 2020 *)
%o (PARI) is(n)=issquare(sigma(n)+numdiv(n))&&issquare(sigma(n+1)+ numdiv(n+1)) \\ _Charles R Greathouse IV_, Apr 09 2013
%Y Cf. A000005, A000203, A007503.
%K nonn
%O 1,1
%A _Jayanta Basu_, Apr 09 2013
|
