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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A129486 A203047 A309190 * A234996 A234389 A234393

Adjacent sequences: A074385 A074386 A074387 * A074389 A074390 A074391

Keyword

nonn,changed

Author

Labos Elemer, Aug 22 2002

Extensions

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

Status

approved