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A287472 Triangular numbers k such that phi(k) is also a triangular number, where phi(k) is the Euler totient function (A000010). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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, ...

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A324319 A246886 A258167 * A350368 A183672 A183664

Adjacent sequences:  A287469 A287470 A287471 * A287473 A287474 A287475

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 25 2017

STATUS

approved

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Last modified August 8 12:30 EDT 2022. Contains 356009 sequences. (Running on oeis4.)