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A074388
Numbers of the form 2*k^2 such that sigma(2*k^2) is an odd square.
3
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 22 2002
EXTENSIONS
a(19)-a(22) from Amiram Eldar, Aug 13 2024
STATUS
approved