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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A321723 A282763 A013338 * A143243 A157812 A218164
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)