A287473 Triangular numbers k such that phi(k) is a square number, where phi(k) is the Euler totient function (A000010).

1, 10, 136, 630, 2016, 7875, 9180, 18915, 32896, 37128, 46056, 58311, 66430, 103740, 131841, 198135, 225456, 301476, 323610, 332520, 408156, 499500, 738720, 786885, 839160, 862641, 922761, 924120, 1065070, 1079715, 1183491, 1385280, 1851850, 1906128, 1925703

Offset: 1

Author

Amiram Eldar, May 25 2017

Keywords

• nonn

Comments

The indices of these triangular numbers are: 1, 4, 16, 35, 63, 125, 135, 194, 256, 272, 303, 341, 364, 455, 513, 629, 671, 776, 804, 815, 903, 999, 1215, 1254, 1295, 1313, 1358, 1359, 1459, 1469, 1538, 1664, 1924, 1952, 1962, ... and their phi values are the squares of: 1, 2, 8, 12, 24, 60, 48, 96, 128, 96, 120, 180, 144, 144, 288, 288, 240, 288, 264, 288, 336, 360, 432, 600, 432, 720, 720, 480, 648, 672, 864, 576, 720, 720, 1080, ...

Similar to A115910, since A115910(n)^2 are squares whose phi is a triangular number.

Examples

			136=16*17/2 is triangular, phi(136)=64=8^2 is a square, thus 136 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A000217, A000290, A039770, A115910, A256151.

Intersection of A000217 and A039770.

Programs

Mathematica

Select[Accumulate[Range[1000]],IntegerQ[Sqrt[EulerPhi[#]]]&]

PARI

isok(n) = ispolygonal(n, 3) && issquare(eulerphi(n)); \\ Michel Marcus, May 25 2017