A055515 a(n) = (2^n - 1)/product(2^p - 1) where the product is over all distinct primes p that divide n.

1, 1, 1, 5, 1, 3, 1, 85, 73, 11, 1, 195, 1, 43, 151, 21845, 1, 12483, 1, 11275, 2359, 683, 1, 798915, 1082401, 2731, 19173961, 704555, 1, 1649373, 1, 1431655765, 599479, 43691, 8727391, 3272356035, 1, 174763, 9588151, 11822705675, 1, 1649061309, 1

Offset: 1

Author

Leroy Quet, Jul 03 2000

Keywords

• easy
• nonn

Examples

			a(12) = (2^12 -1)/((2^2 -1) (2^3 -1)) = 195.
		

Links

• John Tyler Rascoe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055977.

Programs

Mathematica

Table[(2^n-1)/Times@@(2^#-1&/@FactorInteger[n][[;;,1]]),{n,50}] (* Harvey P. Dale, Jan 18 2025 *)

PARI

a(n) = my(f = factor(n)); (2^n-1)/prod(i=1, #f~, 2^f[i, 1] -1); \\ Michel Marcus, May 18 2014

Formula

For p prime, a(p) = 1. - Michel Marcus, May 18 2014

For p prime, a(p^2) = A051156(n). - Michel Marcus, May 18 2014