login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000415 Numbers that are the sum of 2 but no fewer nonzero squares. 17
2, 5, 8, 10, 13, 17, 18, 20, 26, 29, 32, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 136, 137, 145, 146, 148, 149, 153, 157, 160, 162, 164, 170, 173, 178, 180, 181 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Only these numbers can occur as discriminants of quintic polynomials with solvable Galois group F20. - Artur Jasinski, Oct 25 2007
Complement of A022544 in the nonsquare positive integers A000037. - Max Alekseyev, Jan 21 2010
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
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
{ A000404 } minus { A134422 }. - Artur Jasinski, Oct 25 2007
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
A000415_list = list(islice(A000415_gen(), 20)) # Chai Wah Wu, Aug 01 2023
CROSSREFS
Sequence in context: A000404 A025284 A140328 * A172000 A096691 A202057
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 17:14 EDT 2024. Contains 374552 sequences. (Running on oeis4.)