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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 17 22:59 EDT 2019. Contains 326059 sequences. (Running on oeis4.)