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

0, 1, 6, 11, 18, 27, 37, 49, 63, 114, 159, 183, 210, 238, 268, 299, 333, 368, 405, 443, 484, 526, 571, 663, 714, 765, 820, 874, 931, 990, 1049, 1110, 1176, 1241, 1307, 1380, 1451, 1523, 1598, 1673, 1834, 1916, 2001, 2174, 2266, 2355, 2544, 2643, 2737, 2837

Offset: 1

Author

David Garber, Nov 13 2002

Keywords

• nonn

Comments

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,....

Examples

			Since pi(6)=3 and 6+3=9 is a square, so 6 belongs to the sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000720, A077510.

Programs

Maple

q:= n-> issqr(n+numtheory[pi](n)):
select(q, [$0..3000])[];  # Alois P. Heinz, Oct 27 2021

Mathematica

Select[Range[0,3000],IntegerQ[Sqrt[#+PrimePi[#]]]&] (* Harvey P. Dale, Feb 01 2014 *)

PARI

isok(n) = issquare(n + primepi(n)); \\ Michel Marcus, Feb 01 2014

Extensions

I put "more" to indicate that the two subsidiary sequences should be detached and made into separate sequences. - N. J. A. Sloane.

Offset changed and terms prepended by Harvey P. Dale and Michel Marcus, Feb 01 2014

Offset 1 from Alois P. Heinz, Oct 27 2021