login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054520 Let S = {1,5,9,13,..., 4n+1, ...} and call p in S an S-prime if p>1 and the only divisors of p in S are 1 and p; sequence gives elements of S that are not S-primes. 5
1, 25, 45, 65, 81, 85, 105, 117, 125, 145, 153, 165, 169, 185, 189, 205, 221, 225, 245, 261, 265, 273, 285, 289, 297, 305, 325, 333, 345, 357, 365, 369, 377, 385, 405, 425, 429, 441, 445, 465, 477, 481, 485, 493, 505, 513, 525, 533, 545, 549, 561, 565, 585 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The set S is a standard example of a set where unique factorization does not hold.

With the exception A054520(1)=1, numbers of the form 4*(m + n + 4 m n)+1 (m,n>0). No such number can be prime because 4*(m + n + 4 m n)+1=(4m+1)(4n+1). - Artur Jasinski, Sep 22 2008

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 101, problem 1.

LINKS

William A. Tedeschi, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Hilbert Number

EXAMPLE

49 is an S-prime.

MATHEMATICA

a = {}; Do[Do[AppendTo[a, 4(m + n + 4 m n)+1], {m, 1, 100}], {n, 1, 100}]; Union[a] (* Artur Jasinski, Sep 22 2008 *)

PROG

(PARI) ok(n)={if(n%4==1, my(f=factor(n)); 2<>sum(i=1, #f~, f[i, 2]*if(f[i, 1]%4==3, 1, 2)), 0)} \\ Andrew Howroyd, Nov 25 2018

CROSSREFS

Cf. A057948, A057949, A057950.

Sequence in context: A105507 A015911 A188005 * A192261 A038811 A028505

Adjacent sequences:  A054517 A054518 A054519 * A054521 A054522 A054523

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Apr 09 2000

EXTENSIONS

More terms from James A. Sellers, Apr 11 2000

Offset corrected by Andrew Howroyd, Nov 25 2018

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 15:20 EST 2019. Contains 320336 sequences. (Running on oeis4.)