A287472 - OEIS

%I #12 May 28 2017 09:33:55

%S 1,231,1035,6786,190036,193131,766941,1237951,1348903,3069003,3396921,

%T 8034036,9152781,11875501,15694003,28001386,29587278,35149920,

%U 61643856,63196903,130758706,178161126,198214005,227751153,268111746,339210081,402102261,654224878

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

%C 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, ...

%C 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, ...

%H Amiram Eldar, <a href="/A287472/b287472.txt">Table of n, a(n) for n = 1..100</a>

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

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

%o (PARI) isok(n) = ispolygonal(n, 3) && ispolygonal(eulerphi(n), 3); \\ _Michel Marcus_, May 25 2017

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

%K nonn

%O 1,2

%A _Amiram Eldar_, May 25 2017