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A100587 Number of nonempty subsets of divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 8 04:26 EDT 2020. Contains 333312 sequences. (Running on oeis4.)