A074388 Numbers of the form 2*k^2 such that sigma(2*k^2) is an odd square.

195938, 224450, 13645088, 15870978, 18180450, 29184800, 1105252128, 2363968800, 2686005218, 2917410498, 3564550178, 5056357922, 8442721568, 10814792450, 18587462432, 21292224800, 48666384162, 140836104992, 212352534818, 217566422658, 288728564418, 315325993248

Offset: 1

Author

Labos Elemer, Aug 22 2002

Keywords

• nonn

Comments

No terms whose sum of divisors is a square of a prime below 10^12 were found.

Examples

			195938 = 2*313^2 and sigma(195938) = 294849 = 543^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..200 (calculated using the b-file at A097023)

Crossrefs

Cf. A000203, A001248, A028982, A074386, A097023.

Programs

Mathematica

Do[s=DivisorSigma[1, 2*(n^2)]; If[IntegerQ[Sqrt[s]]&&Mod[s, 2]==1, Print[2*(n^2)]], {n, 1, 10000000}]

Formula

a(n) = 2*A097023(n)^2. - Amiram Eldar, Aug 13 2024

Extensions

a(19)-a(22) from Amiram Eldar, Aug 13 2024