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
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)
Programs
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Haskell
a008847 n = a008847_list !! (n-1) a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..] -- Reinhard Zumkeller, Mar 27 2013
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Maple
with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od;
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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 *) -
PARI
is_A008847(n)=issquare(sigma(n^2)) \\ M. F. Hasler, Oct 23 2010
Formula
a(n) = sqrt(A008848(n)). - Zak Seidov, May 01 2016
Comments