OFFSET
1,1
COMMENTS
Only these numbers can occur as discriminants of quintic polynomials with solvable Galois group F20. - Artur Jasinski, Oct 25 2007
Nonsquare positive integers D such that Pell equation y^2 - D*x^2 = -1 has rational solutions. - Max Alekseyev, Mar 09 2010
Nonsquares for which all 4k+3 primes in the integer's canonical form occur with even multiplicity. - Ant King, Nov 02 2010
REFERENCES
E. Grosswald, Representation of Integers as Sums of Squares, Springer-Verlag, New York Inc., (1985), p.15. - Ant King, Nov 02 2010
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172. - Ant King, Nov 02 2010
Eric Weisstein's World of Mathematics, Square Number
FORMULA
MATHEMATICA
c = {}; Do[Do[k = a^2 + b^2; If[IntegerQ[Sqrt[k]], Null, AppendTo[c, k]], {a, 1, 100}], {b, 1, 100}]; Union[c] (* Artur Jasinski, Oct 25 2007 *)
Select[Range[181], Length[PowersRepresentations[ #, 2, 2]]>0 && !IntegerQ[Sqrt[ # ]] &] (* Ant King, Nov 02 2010 *)
PROG
(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return(0))); !issquare(n) \\ Charles R Greathouse IV, Feb 07 2017
(Python)
from itertools import count, islice
from sympy import factorint
def A000415_gen(startvalue=2): # generator of terms >= startvalue
for n in count(max(startvalue, 2)):
f = factorint(n).items()
if any(e&1 for p, e in f if p&3<3) and not any(e&1 for p, e in f if p&3==3):
yield n
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved