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A117949
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Index of pentagonal numbers whose sum of divisors is square.
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2
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MAPLE
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with(numtheory): select(n-> sqrt(sigma(n*(3*n-1)/2))::integer, [$1..2200])[]; # Emeric Deutsch, Apr 06 2006
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(n) = issquare(sigma(n*(3*n-1)/2)); \\ Michel Marcus, Aug 17 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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