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

1,2

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Wasin So, Integral circulant graphs, Discr. Math. 306 (1) (2006) 153-158

Formula

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

Example

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

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 *)

Prog

(PARI) a(n) = 2^(numdiv(n)) - 1; \\ Michel Marcus, Dec 15 2013
(Haskell)
a100587 = (subtract 1) . (2 ^) . a000005'
-- Reinhard Zumkeller, Jun 27 2015

Crossrefs

Cf. A000005, A066781, A100371.

Cf. A119347.

Sequence in context: A156838 A274845 A324048 * A324548 A249383 A187419

Adjacent sequences: A100584 A100585 A100586 * A100588 A100589 A100590

Keyword

nonn,easy

Author

Labos Elemer, Dec 01 2004

Status

approved