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

%I A245197 #21 Feb 08 2023 09:28:30
%S A245197 1,8,85,125,365,445,533,629,965,1685,1800,1853,2340,2605,2813,3029,
%T A245197 3973,4765,5045,5220,5629,5933,6245,6893,8285,8653,11029,11453,11885,
%U A245197 12773,14165,15133,16645,17165,17460,17693,20453,21029,22205,22805,23413,24653,27229
%N A245197 Numbers n where tau(n) and n-tau(n) are perfect squares, with tau(n) the number of divisors of n (A000005).
%C A245197 Subsequence of A036436. - _Michel Marcus_, Jul 15 2014
%C A245197 Intersection of A036436 and A245388. - _Robert Israel_, Jul 20 2014
%H A245197 Jens Kruse Andersen, <a href="/A245197/b245197.txt">Table of n, a(n) for n = 1..2989</a>
%p A245197 filter:= proc(n) local t;
%p A245197   t:= numtheory:-tau(n);
%p A245197   issqr(t) and issqr(n-t)
%p A245197 end proc;
%p A245197 select(filter, [$1..10^5]); # _Robert Israel_, Jul 20 2014
%t A245197 okQ[n_] := With[{t = DivisorSigma[0, n]}, IntegerQ@Sqrt[t] && IntegerQ@Sqrt[n-t]];
%t A245197 Select[Range[10^5], okQ] (* _Jean-François Alcover_, Feb 08 2023 *)
%o A245197 (PARI) isok(n) = issquare(numdiv(n)) && issquare(n-numdiv(n)); \\ _Michel Marcus_, Jul 15 2014
%Y A245197 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).
%K A245197 nonn
%O A245197 1,2
%A A245197 _Reinhard Muehlfeld_, Jul 13 2014