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a(n) = number of finite sequences using numbers drawn from (1,2,3,...,n), using each number at most once, where each number in a finite sequence is not coprime to the previous number, and each finite sequence must continued if possible. (See example.)
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%I #9 Mar 11 2014 01:32:51

%S 1,2,3,4,5,13,14,43,79,457,458,5145,5146,38237,259920,1702869,1702870,

%T 28603827,28603828,402599903,3319634320,34246343007,34246343008

%N a(n) = number of finite sequences using numbers drawn from (1,2,3,...,n), using each number at most once, where each number in a finite sequence is not coprime to the previous number, and each finite sequence must continued if possible. (See example.)

%F a(p)=a(p-1)+1 for all primes p.

%e For n = 7, we have these 14 finite sequences:

%e 1;

%e 2,4,6,3;

%e 2,6,3;

%e 2,6,4;

%e 3,6,2,4;

%e 3,6,4,2;

%e 4,2,6,3;

%e 4,6,2;

%e 4,6,3;

%e 5;

%e 6,2,4;

%e 6,3;

%e 6,4,2;

%e 7

%K more,nonn

%O 1,2

%A _Leroy Quet_, Mar 24 2010

%E More terms from _Sean A. Irvine_, Nov 25 2010