A004729 Divisors of 2^32 - 1 (for a(1) to a(31), the 31 regular polygons with an odd number of sides constructible with ruler and compass).

1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 65537, 196611, 327685, 983055, 1114129, 3342387, 5570645, 16711935, 16843009, 50529027, 84215045, 252645135, 286331153, 858993459, 1431655765, 4294967295

Offset

0,2

Comments

The 32 divisors of the product of the 5 known Fermat primes.

The only known odd numbers whose totient is a power of 2. - Labos Elemer, Dec 06 2000

Equals first 32 members of A001317. Also, equals first 32 members of A053576. - Omar E. Pol, Dec 10 2008

Omitting the first term a(0)=1 gives A045544 (the number of sides of constructible odd-sided regular polygons.)

References

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, New York, 1996; see p. 140.

Links

Table of n, a(n) for n=0..31.

Eric Weisstein's World of Mathematics, Regular Polygon, Sierpiński Sieve, Constructible Polygon

OEIS Wiki, Constructible odd-sided polygons

OEIS Wiki, Sierpinski's triangle

Index entries for sequences related to divisors of numbers

Mathematica

Divisors[2^32-1]

Prog

(PARI) divisors(1<<32-1)

Crossrefs

Essentially same as A045544.

Cf. A000010, A000215, A001317, A003401, A003527, A004169, A004729, A019434, A045544, A047999, A053576, A054432.

Sequence in context: A319583 A094358 A003527 * A045544 A001317 A053576

Adjacent sequences: A004726 A004727 A004728 * A004730 A004731 A004732

Keyword

nonn,fini,full,easy

Author

N. J. A. Sloane

Extensions

Edited by Daniel Forgues, Jun 17 2011

Status

approved