A100587 - OEIS

%I #20 Nov 03 2018 10:35:14

%S 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,

%T 63,3,255,3,63,15,15,15,511,3,15,15,255,3,255,3,63,63,15,3,1023,7,63,

%U 15,63,3,255,15,255,15,15,3,4095,3,15,63,127,15,255,3,63,15,255,3,4095,3

%N Number of nonempty subsets of divisors of n.

%C A119347(n) <= a(n). - _Reinhard Zumkeller_, Jun 27 2015

%H Reinhard Zumkeller, <a href="/A100587/b100587.txt">Table of n, a(n) for n = 1..10000</a>

%H Wasin So, <a href="https://doi.org/10.1016/j.disc.2005.11.006">Integral circulant graphs</a>, Discr. Math. 306 (1) (2006) 153-158

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

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

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

%t Table[2^DivisorSigma[0, n] - 1, {n, 73}] (* _Michael De Vlieger_, Dec 11 2015 *)

%o (PARI) a(n) = 2^(numdiv(n)) - 1; \\ _Michel Marcus_, Dec 15 2013

%o (Haskell)

%o a100587 = (subtract 1) . (2 ^) . a000005'

%o -- _Reinhard Zumkeller_, Jun 27 2015

%Y Cf. A000005, A066781, A100371.

%Y Cf. A119347.

%K nonn,easy

%O 1,2

%A _Labos Elemer_, Dec 01 2004