A287472 Triangular numbers k such that phi(k) is also a triangular number, where phi(k) is the Euler totient function (A000010).

1, 231, 1035, 6786, 190036, 193131, 766941, 1237951, 1348903, 3069003, 3396921, 8034036, 9152781, 11875501, 15694003, 28001386, 29587278, 35149920, 61643856, 63196903, 130758706, 178161126, 198214005, 227751153, 268111746, 339210081, 402102261, 654224878

Offset: 1

Author

Amiram Eldar, May 25 2017

Keywords

• nonn

Comments

The indices of these triangular numbers are: 1, 21, 45, 116, 616, 621, 1238, 1573, 1642, 2477, 2606, 4008, 4278, 4873, 5602, 7483, 7692, 8384, 11103, 11242, 16171, 18876, 19910, 21342, 23156, 26046, 28358, 36172, 46196, 46621, 67572, 72816, ...

The indices of the triangular phi values are: 1, 15, 32, 63, 384, 495, 927, 1440, 1599, 1856, 2015, 2240, 3200, 4640, 5375, 4895, 4095, 4095, 6400, 9855, 10880, 9855, 13824, 16128, 12095, 19520, 21504, 25344, 25983, 45584, 37184, 40959, ...

Examples

			231 = 21*22/2 is triangular, phi(231)=120=15*16/2 is also triangular, thus 231 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000010, A000217, A083674, A083675, A115910, A116541.

Programs

Mathematica

triQ[n_] := IntegerQ@Sqrt[8n+1]; Select[Accumulate[Range[1000]], triQ[EulerPhi[#]]&]

PARI

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