cp's OEIS Frontend

A187092 Number of nonempty subsets S of {1, 2, ..., n} with pairwise coprime elements that are maximal with respect to inclusion of elements < max(S).

%I A187092 #15 Mar 27 2017 18:32:23
%S A187092 1,2,3,4,6,7,9,10,13,15,21,22,28,30,33,35,43,44,52,54,58,60,68,69,77,
%T A187092 81,89,95,119,120,144,150,160,166,181,183,213,219,229,232,262,264,294,
%U A187092 300,305,311,341,343,373,379,399,411,471,475,505,511,531
%N A187092 Number of nonempty subsets S of {1, 2, ..., n} with pairwise coprime elements that are maximal with respect to inclusion of elements < max(S).
%H A187092 Alois P. Heinz, <a href="/A187092/b187092.txt">Table of n, a(n) for n = 1..10000</a>
%e A187092 a(8) = 10; all nonempty subsets S of {1, 2, ..., 8} with pairwise coprime elements that are maximal with respect to inclusion of elements < max(S) are: {1}, {1,2}, {1,2,3}, {1,3,4}, {1,5,6}, {1,2,3,5}, {1,3,4,5}, {1,2,3,5,7}, {1,3,4,5,7}, {1,3,5,7,8}.
%p A187092 with(numtheory):
%p A187092 b:= n-> mul(ilog[j](n), j={ithprime(i)$i=1..pi(n)} minus factorset(n)):
%p A187092 a:= proc(n) option remember; b(n) +`if`(n<2, 0, a(n-1)) end:
%p A187092 seq(a(n), n=1..80);
%t A187092 b[n_] := Product[Log[p, n] // Floor, {p, Select[Range[n-1], PrimeQ[#] && GCD[n, #] == 1&]}];
%t A187092 A187092 = Array[b, 100] // Accumulate (* _Jean-François Alcover_, Mar 27 2017, adapted from Maple *)
%Y A187092 Partial sums of A186994.
%K A187092 nonn
%O A187092 1,2
%A A187092 _Alois P. Heinz_, Mar 04 2011