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A073945 Numbers n such that n + pi(n) is a square.

%I A073945 #34 Oct 27 2021 12:08:36
%S A073945 0,1,6,11,18,27,37,49,63,114,159,183,210,238,268,299,333,368,405,443,
%T A073945 484,526,571,663,714,765,820,874,931,990,1049,1110,1176,1241,1307,
%U A073945 1380,1451,1523,1598,1673,1834,1916,2001,2174,2266,2355,2544,2643,2737,2837
%N A073945 Numbers n such that n + pi(n) is a square.
%C A073945 The corresponding sequence of squares is: 0,1,9,16,25,36,49,64,81,144,196,225,256,289,324,361,400,441,484,529,576,625,676,784,841,900,961,1024,1089,1156,1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,... and the sequence of their square roots is: 0,1,3,4,5,6,7,8,9,12,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,46,47,48,50,51,52,54,55,56,57,58,59,60,61,62,63,64,65,66,68,69,70,....
%H A073945 Vincenzo Librandi, <a href="/A073945/b073945.txt">Table of n, a(n) for n = 1..500</a>
%e A073945 Since pi(6)=3 and 6+3=9 is a square, so 6 belongs to the sequence.
%p A073945 q:= n-> issqr(n+numtheory[pi](n)):
%p A073945 select(q, [$0..3000])[];  # _Alois P. Heinz_, Oct 27 2021
%t A073945 Select[Range[0,3000],IntegerQ[Sqrt[#+PrimePi[#]]]&] (* _Harvey P. Dale_, Feb 01 2014 *)
%o A073945 (PARI) isok(n) = issquare(n + primepi(n)); \\ _Michel Marcus_, Feb 01 2014
%Y A073945 Cf. A000720, A077510.
%K A073945 nonn
%O A073945 1,3
%A A073945 _David Garber_, Nov 13 2002
%E A073945 I put "more" to indicate that the two subsidiary sequences should be detached and made into separate sequences. - _N. J. A. Sloane_.
%E A073945 Offset changed and terms prepended by _Harvey P. Dale_ and _Michel Marcus_, Feb 01 2014
%E A073945 Offset 1 from _Alois P. Heinz_, Oct 27 2021