A117949 Index of pentagonal numbers whose sum of divisors is square.

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

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