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A008847
Numbers k such that sum of divisors of k^2 is a square.
11
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
KEYWORD
nonn,nice,easy
STATUS
approved