login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A109511 Number of subsets of the first n numbers having a common divisor greater than 1. 2

%I

%S 0,1,2,4,5,10,11,19,23,40,41,79,80,145,164,292,293,577,578,1096,1163,

%T 2188,2189,4357,4373,8470,8726,16924,16925,33832,33833,66601,67628,

%U 133165,133244,266332,266333,528478,532577,1056985,1056986,2113717

%N Number of subsets of the first n numbers having a common divisor greater than 1.

%C a(n) = 2^n - A085945(n) - 1 = A000225 - A085945(n);

%C a(n) - a(n-1) = 1 iff n is prime;

%C a(p^e) = a(p^e - 1) + 2^(p^(e-1) - 1) for p prime, e>0;

%C a(p*q) = a(p*q - 1) + 2^(p-1) + 2^(q-1) - 1 for primes p<>q.

%H Alois P. Heinz, <a href="/A109511/b109511.txt">Table of n, a(n) for n = 1..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Inclusion-ExclusionPrinciple.html">Inclusion-Exclusion Principle</a>

%F a(n) = Sum(-mu(k) * (2^floor(n/k)-1): 1<k<=n), mu=A008683.

%e a(6) = #{{2}, {3}, {4}, {5}, {6}, {2,4}, {2,6}, {3,6}, {4,6}, {2,4,6}} = 10.

%t Table[Sum[-MoebiusMu[k] (2^Floor[n/k] - 1), {k, 2, n}], {n, 1, 41}] (* _Geoffrey Critzer_, Jan 03 2012 *)

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Jul 01 2005

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 20:48 EST 2017. Contains 295856 sequences.