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 A287473 Triangular numbers k such that phi(k) is a square number, where phi(k) is the Euler totient function (A000010). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)