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).

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, 81, 89, 95, 119, 120, 144, 150, 160, 166, 181, 183, 213, 219, 229, 232, 262, 264, 294, 300, 305, 311, 341, 343, 373, 379, 399, 411, 471, 475, 505, 511, 531

Offset: 1

Author

Alois P. Heinz, Mar 04 2011

Keywords

• nonn

Examples

			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}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Partial sums of A186994.

Programs

Maple

with(numtheory):
b:= n-> mul(ilog[j](n), j={ithprime(i)$i=1..pi(n)} minus factorset(n)):
a:= proc(n) option remember; b(n) +`if`(n<2, 0, a(n-1)) end:
seq(a(n), n=1..80);

Mathematica

b[n_] := Product[Log[p, n] // Floor, {p, Select[Range[n-1], PrimeQ[#] && GCD[n, #] == 1&]}];
A187092 = Array[b, 100] // Accumulate (* Jean-François Alcover, Mar 27 2017, adapted from Maple *)