

A008848


Squares whose sum of divisors is a square.


8



1, 81, 400, 32400, 1705636, 3648100, 138156516, 295496100, 1055340196, 1476326929, 2263475776, 2323432804, 2592846400, 2661528100, 7036525456, 10994571025, 17604513124, 39415749156, 61436066769, 85482555876, 90526367376, 97577515876, 98551417041
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OFFSET

1,2


COMMENTS

Solutions to sigma(x^2) = (2k+1)^2.  Labos Elemer, Aug 22 2002
Intersection of A006532 and A000290. The product of any two coprime terms is also in this sequence.  Charles R Greathouse IV, May 10 2011
Also intersection of A069070 and A000290.  Michel Marcus, Oct 06 2013


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..400


EXAMPLE

n=32400: sigma[32400] = 116281 = 341^2 = 121*961.


MATHEMATICA

Do[s=DivisorSigma[1, n^2]; If[IntegerQ[Sqrt[s]]&&Mod[s, 2]==1, Print[n^2]], {n, 1, 10000000}] (* Labos Elemer *)
Select[Range[320000]^2, IntegerQ[Sqrt[DivisorSigma[1, #]]]&] (* Harvey P. Dale, Feb 22 2015 *)


PROG

(PARI) for(n=1, 1e6, if(issquare(sigma(n^2)), print1(n^2", "))) \\ Charles R Greathouse IV, May 10 2011


CROSSREFS

a(n) = A008847(n)^2.
Cf. A028982, A001248, A000203.
Sequence in context: A017498 A097025 A074387 * A237182 A237176 A102741
Adjacent sequences: A008845 A008846 A008847 * A008849 A008850 A008851


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



