OFFSET
1,1
COMMENTS
Numbers k such that A000203(k) = -1 + m^2 for some m.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 02 2001
EXTENSIONS
Minor edits from Franklin T. Adams-Watters, Aug 29 2009
STATUS
approved