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

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full
• easy

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

• 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

Crossrefs

Essentially same as A045544.

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

Programs

Mathematica

Divisors[2^32-1]

PARI

divisors(1<<32-1)

Extensions

Edited by Daniel Forgues, Jun 17 2011