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A063531 Numbers k such that sigma(k) + 1 is a square. 2
2, 7, 8, 14, 15, 23, 32, 33, 35, 47, 54, 56, 57, 60, 72, 78, 79, 84, 87, 92, 95, 120, 123, 124, 128, 138, 143, 154, 165, 167, 174, 184, 190, 196, 213, 223, 235, 242, 252, 253, 258, 267, 295, 312, 315, 319, 323, 327, 348, 359, 375, 378, 380, 393, 412, 423, 439 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

A000203(k) = -1 + m^2 for some m.

EXAMPLE

If k = p(p+2) is a product of twin primes (from A037074), then sigma(k) + 1 = 1 + (p+1)(p+3) = (p+2)^2, square of the larger twin. Other solutions can be either special primes = m^2 - 2 or composites like 120: sigma(120) = 120 + 60 + ... + 1 = 360 = 19^2 - 1. Square number solution is, e.g., 196: sigma(196) = 399 = 20^2 - 1.

MATHEMATICA

Select[Range[500], IntegerQ[Sqrt[DivisorSigma[1, #]+1]]&] (* Harvey P. Dale, Jul 02 2021 *)

PROG

(PARI) { n=0; for (a=1, 10^9, if (issquare(sigma(a) + 1), write("b063531.txt", n++, " ", a); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 25 2009

CROSSREFS

Cf. A000010, A000203, A015722, A028871, A037074.

Sequence in context: A308918 A226819 A270104 * A063771 A064293 A063729

Adjacent sequences:  A063528 A063529 A063530 * A063532 A063533 A063534

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 02 2001

EXTENSIONS

Minor edits from Franklin T. Adams-Watters, Aug 29 2009

STATUS

approved

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Last modified May 29 05:00 EDT 2022. Contains 354122 sequences. (Running on oeis4.)