|
|
A224441
|
|
Numbers n such that sigma(n)+d(n) and sigma(n+1)+d(n+1) are perfect squares.
|
|
1
|
|
|
61, 2369, 4469, 8460, 13208, 44790, 162734, 281560, 283938, 334469, 500465, 533045, 609953, 871853, 962247, 1317885, 1741445, 1792745, 2499845, 3013246, 4099031, 5646629, 7009389, 7012135, 8396781, 8740480, 8822093, 11146381, 11957693, 15002679, 18895694
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
61 is in the list since sigma(61)+d(61)=64 and sigma(62)+d(62)=100.
|
|
MATHEMATICA
|
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
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 *)
|
|
PROG
|
(PARI) is(n)=issquare(sigma(n)+numdiv(n))&&issquare(sigma(n+1)+ numdiv(n+1)) \\ Charles R Greathouse IV, Apr 09 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|