The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A004613 Numbers that are divisible only by primes congruent to 1 mod 4. 24
 1, 5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 73, 85, 89, 97, 101, 109, 113, 125, 137, 145, 149, 157, 169, 173, 181, 185, 193, 197, 205, 221, 229, 233, 241, 257, 265, 269, 277, 281, 289, 293, 305, 313, 317, 325, 337, 349, 353, 365, 373, 377, 389, 397, 401, 409, 421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also gives solutions z to x^2+y^2=z^4 with gcd(x,y,z)=1 and x,y,z positive. - John Sillcox (johnsillcox(AT)hotmail.com), Feb 20 2004 A065338(a(n)) = 1. - Reinhard Zumkeller, Jul 10 2010 Product(A079260(A027748(a(n),k)): k=1..A001221(a(n))) = 1. - Reinhard Zumkeller, Jan 07 2013 A062327(a(n))=A000005(a(n))^2. (These are the only numbers that satisfy this equation) - Benedikt Otten, May 22 2013 Numbers that are positive integer divisors of 1 + 4*x^2 where x is a positive integer. - Michael Somos, Jul 26 2013 Numbers n such that there is a "knight's move" of Euclidean distance sqrt(n) which allows the whole of the 2D lattice to be reached. For example, a knight which travels 4 units in any direction and then 1 unit at right angles to the first direction moves a distance sqrt(17) for each move. This knight can reach every square of an infinite chessboard. REFERENCES David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 David Broadhurst and Wadim Zudilin, A magnetic double integral, arXiv:1708.02381 [math.NT], 2017. See p. 7 'trichoplax', pseudonymous Stack Exchange user, N-movers: How much of the infinite board can I reach? FORMULA Numbers of the form x^2+y^2 where x is even, y is odd and gcd(x, y) = 1. MAPLE isA004613 := proc(n)     local p;     for p in numtheory[factorset](n) do         if modp(p, 4) <> 1 then             return false;         end if;     end do:     true; end proc: for n from 1 to 200 do     if isA004613(n) then         printf("%d, ", n) ;     end if; end do: # R. J. Mathar, Nov 17 2014 MATHEMATICA ok[1] = True; ok[n_] := And @@ (Mod[#, 4] == 1 &) /@ FactorInteger[n][[All, 1]]; Select[Range[421], ok] (* Jean-François Alcover, May 05 2011 *) Select[Range[500], Union[Mod[#, 4]&/@(FactorInteger[#][[All, 1]])]=={1}&] (* Harvey P. Dale, Mar 08 2017 *) PROG (PARI) for(n=1, 1000, if(sumdiv(n, d, isprime(d)*if((d-1)%4, 1, 0))==0, print1(n, ", "))) (PARI) is(n)=n%4==1 && factorback(factor(n)[, 1]%4)==1 \\ Charles R Greathouse IV, Sep 19 2016 (MAGMA) [n: n in [1..500] | forall{d: d in PrimeDivisors(n) | d mod 4 eq 1}]; // Vincenzo Librandi, Aug 21 2012 (Haskell) a004613 n = a004613_list !! (n-1) a004613_list = filter (all (== 1) . map a079260 . a027748_row) [1..] -- Reinhard Zumkeller, Jan 07 2013 CROSSREFS Subsequence of A000404; A002144 is a subsequence. Essentially same as A008846. Cf. A004614. Sequence in context: A087445 A020882 A081804 * A008846 A162597 A120960 Adjacent sequences:  A004610 A004611 A004612 * A004614 A004615 A004616 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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

Last modified August 12 01:37 EDT 2020. Contains 336434 sequences. (Running on oeis4.)