|
| |
|
|
A008847
|
|
Numbers n such that sum of divisors of n^2 is a square.
|
|
8
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| These are the square roots of squares in A006532. [From M. F. Hasler (MHasler(AT)univ-ag.fr), 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
| Zak Seidov, Table of n, a(n) for n=1..161; a(n)<10^8
|
|
|
FORMULA
| A163763(n) = sqrt(sigma(A008847(n)^2)). - M. F. Hasler, Oct 16 2010.
|
|
|
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 (* From Jean-François Alcover, May 05 2011 *)
Select[Range[1000000], IntegerQ[Sqrt[DivisorSigma[1, #^2]]]&] (* From Harvey P. Dale, Aug 22 2011 *)
|
|
|
PROG
| (PARI) is_A008847(n)=issquare(sigma(n^2)) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 23 2010]
|
|
|
CROSSREFS
| Cf. A008848, A008849, A008850, A163763.
Sequence in context: A013573 A146388 A013338 * A143243 A157812 A161326
Adjacent sequences: A008844 A008845 A008846 * A008848 A008849 A008850
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
