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A100587
Number of nonempty subsets of divisors of n.
17
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
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
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Dec 01 2004
STATUS
approved