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 A117949 Index of pentagonal numbers whose sum of divisors is square. 2
 1, 4, 7, 12, 21, 23, 27, 31, 71, 79, 89, 151, 168, 199, 223, 232, 239, 263, 311, 324, 336, 345, 359, 390, 463, 479, 497, 540, 599, 743, 751, 823, 858, 863, 911, 991, 1031, 1063, 1103, 1151, 1302, 1303, 1343, 1399, 1471, 1540, 1583, 1687, 1759, 1802, 1823 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS n such that A117948(n) is in A000290. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE a(1) = 1 because sigma[1*(3*1-1)/2)] = 1 = 1^2. a(2) = 4 because sigma[4*(3*4-1)/2)] = 36 = 6^2. a(3) = 7 because sigma[7*(3*7-1)/2)] = 144 = 12^2. a(4) = 12 because sigma[12*(3*12-1)/2)] = 576 = 24^2. a(5) = 21 because sigma[21*(3*21-1)/2)] = 1024 = 32^2. a(6) = 23 because sigma[23*(3*23-1)/2)] = 1296 = 36^2. a(7) = 27 because sigma[27*(3*27-1)/2)] = 3600 = 60^2. a(8) = 31 because sigma[31*(3*31-1)/2)] = 2304 = 48^2. a(9) = 71 because sigma[71*(3*71-1)/2)] = 11664 = 108^2. MAPLE with(numtheory): select(n-> sqrt(sigma(n*(3*n-1)/2))::integer, [\$1..2200])[]; # Emeric Deutsch, Apr 06 2006 MATHEMATICA s = {}; Do[If[IntegerQ @ Sqrt @ DivisorSigma[1, (3 n - 1)*n/2], AppendTo[s, n]], {n, 1, 2000}]; s (* Amiram Eldar, Aug 17 2019 *) Position[DivisorSigma[1, PolygonalNumber[5, Range[2000]]], _?(IntegerQ[ Sqrt[ #]]&)]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 23 2020 *) PROG (PARI) isok(n) = issquare(sigma(n*(3*n-1)/2)); \\ Michel Marcus, Aug 17 2019 CROSSREFS Cf. A000203, A000217, A000290, A000326, A074285, A083675, A117948. Sequence in context: A020732 A339891 A310793 * A228879 A010901 A187211 Adjacent sequences:  A117946 A117947 A117948 * A117950 A117951 A117952 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Apr 04 2006 EXTENSIONS More terms from Emeric Deutsch, Apr 06 2006 a(0) removed by Amiram Eldar, Aug 17 2019 STATUS approved

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Last modified April 10 19:18 EDT 2021. Contains 342853 sequences. (Running on oeis4.)