A100587 Number of nonempty subsets of divisors of n.

1, 3, 3, 7, 3, 15, 3, 15, 7, 15, 3, 63, 3, 15, 15, 31, 3, 63, 3, 63, 15, 15, 3, 255, 7, 15, 15, 63, 3, 255, 3, 63, 15, 15, 15, 511, 3, 15, 15, 255, 3, 255, 3, 63, 63, 15, 3, 1023, 7, 63, 15, 63, 3, 255, 15, 255, 15, 15, 3, 4095, 3, 15, 63, 127, 15, 255, 3, 63, 15, 255, 3, 4095, 3

Offset: 1

Author

Labos Elemer, Dec 01 2004

Keywords

• nonn
• easy

Comments

A119347(n) <= a(n). - Reinhard Zumkeller, Jun 27 2015

Examples

			For all prime numbers p, a(p)=3, since those subsets are {{1,p},{1},{p}}.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Wasin So, Integral circulant graphs, Discr. Math. 306 (1) (2006) 153-158

Crossrefs

Cf. A000005, A066781, A100371.

Cf. A119347.

Programs

Haskell

a100587 = (subtract 1) . (2 ^) . a000005'
-- Reinhard Zumkeller, Jun 27 2015

Maple

A100587:=n->-1+2^numtheory[tau](n): seq(A100587(n), n=1..100); # Wesley Ivan Hurt, Dec 12 2015

Mathematica

Table[2^DivisorSigma[0, n] - 1, {n, 73}] (* Michael De Vlieger, Dec 11 2015 *)

PARI

a(n) = 2^(numdiv(n)) - 1; \\ Michel Marcus, Dec 15 2013

Formula

a(n) = -1 + 2^tau(n), where tau(n) = DivisorSigma(0, n) = A000005(n).