A008847 Numbers k such that sum of divisors of k^2 is a square.

1, 9, 20, 180, 1306, 1910, 11754, 17190, 32486, 38423, 47576, 48202, 50920, 51590, 83884, 104855, 132682, 198534, 247863, 292374, 300876, 312374, 313929, 334330, 345807, 376095, 428184, 433818, 458280, 464310, 469623, 498892, 623615, 754956, 768460, 787127, 943695, 985369

Offset

1,2

Comments

These are the square roots of squares in A006532. - M. F. Hasler, Oct 23 2010

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 (first 161 terms from Zak Seidov)

Formula

A163763(n) = sqrt(sigma(A008847(n)^2)). - M. F. Hasler, Oct 16 2010

a(n) = sqrt(A008848(n)). - Zak Seidov, May 01 2016

Maple

with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od;

Mathematica

s = {}; Do[ If[IntegerQ[ Sqrt[ DivisorSigma[1, n^2]]], Print[n]; AppendTo[s, n]], {n, 10^6}]; s (* Jean-François Alcover, May 05 2011 *)
Select[Range[1000000], IntegerQ[Sqrt[DivisorSigma[1, #^2]]]&] (* Harvey P. Dale, Aug 22 2011 *)

Prog

(PARI) is_A008847(n)=issquare(sigma(n^2)) \\ M. F. Hasler, Oct 23 2010
(Haskell)
a008847 n = a008847_list !! (n-1)
a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..]
-- Reinhard Zumkeller, Mar 27 2013

Crossrefs

Cf. A008848, A008849, A008850, A163763.

Cf. A000203, A010052, A000290.

Sequence in context: A321723 A282763 A013338 * A143243 A157812 A218164

Adjacent sequences: A008844 A008845 A008846 * A008848 A008849 A008850

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved