cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A100587 Number of nonempty subsets of divisors of n.

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%I A100587 #20 Nov 03 2018 10:35:14
%S A100587 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 A100587 63,3,255,3,63,15,15,15,511,3,15,15,255,3,255,3,63,63,15,3,1023,7,63,
%U A100587 15,63,3,255,15,255,15,15,3,4095,3,15,63,127,15,255,3,63,15,255,3,4095,3
%N A100587 Number of nonempty subsets of divisors of n.
%C A100587 A119347(n) <= a(n). - _Reinhard Zumkeller_, Jun 27 2015
%H A100587 Reinhard Zumkeller, <a href="/A100587/b100587.txt">Table of n, a(n) for n = 1..10000</a>
%H A100587 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 A100587 a(n) = -1 + 2^tau(n), where tau(n) = DivisorSigma(0, n) = A000005(n).
%e A100587 For all prime numbers p, a(p)=3, since those subsets are {{1,p},{1},{p}}.
%p A100587 A100587:=n->-1+2^numtheory[tau](n): seq(A100587(n), n=1..100); # _Wesley Ivan Hurt_, Dec 12 2015
%t A100587 Table[2^DivisorSigma[0, n] - 1, {n, 73}] (* _Michael De Vlieger_, Dec 11 2015 *)
%o A100587 (PARI) a(n) = 2^(numdiv(n)) - 1; \\ _Michel Marcus_, Dec 15 2013
%o A100587 (Haskell)
%o A100587 a100587 = (subtract 1) . (2 ^) . a000005'
%o A100587 -- _Reinhard Zumkeller_, Jun 27 2015
%Y A100587 Cf. A000005, A066781, A100371.
%Y A100587 Cf. A119347.
%K A100587 nonn,easy
%O A100587 1,2
%A A100587 _Labos Elemer_, Dec 01 2004