

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
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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) 153158


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



