A245197 Numbers n where tau(n) and n-tau(n) are perfect squares, with tau(n) the number of divisors of n (A000005).

1, 8, 85, 125, 365, 445, 533, 629, 965, 1685, 1800, 1853, 2340, 2605, 2813, 3029, 3973, 4765, 5045, 5220, 5629, 5933, 6245, 6893, 8285, 8653, 11029, 11453, 11885, 12773, 14165, 15133, 16645, 17165, 17460, 17693, 20453, 21029, 22205, 22805, 23413, 24653, 27229

Offset: 1

Author

Reinhard Muehlfeld, Jul 13 2014

Keywords

• nonn

Comments

Subsequence of A036436. - Michel Marcus, Jul 15 2014

Intersection of A036436 and A245388. - Robert Israel, Jul 20 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..2989

Crossrefs

Cf. A000005 (tau(n)), A049820 (n - tau(n)), A036436 (n such that tau(n) is square), A245388 (n such that n - tau(n) is square).

Programs

Maple

filter:= proc(n) local t;
  t:= numtheory:-tau(n);
  issqr(t) and issqr(n-t)
end proc;
select(filter, [$1..10^5]); # Robert Israel, Jul 20 2014

Mathematica

okQ[n_] := With[{t = DivisorSigma[0, n]}, IntegerQ@Sqrt[t] && IntegerQ@Sqrt[n-t]];
Select[Range[10^5], okQ] (* Jean-François Alcover, Feb 08 2023 *)

PARI

isok(n) = issquare(numdiv(n)) && issquare(n-numdiv(n)); \\ Michel Marcus, Jul 15 2014