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

1,2

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.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Intersection of A000217 and A039770.

Sequence in context: A024135 A050408 A133197 * A240917 A240654 A128862

Adjacent sequences: A287470 A287471 A287472 * A287474 A287475 A287476

Keyword

nonn

Author

Amiram Eldar, May 25 2017

Status

approved