A278078 a(n) is the number of composite numbers prime(n) dominates.

0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17

Offset: 1

Author

Peter Luschny, Dec 28 2016

Keywords

• nonn

Comments

A prime number p dominates a composite numbers c if p is the dominant prime factor of c. A prime factor p of c is dominant if floor(sqrt(p)) > (c/p).

Examples

			53 dominates 106, 159, 212, 265, 318; therefore a(16) = 5.
		

Crossrefs

Cf. A277624.

Programs

Mathematica

a[n_] := Module[{p = Prime[n], c, k}, For[k = 0; c = 2 p, c <= p Sqrt[p], c += p, If[Floor[Sqrt[p]] > c/p, k++]]; k]; Array[a, 74] (* Jean-François Alcover, Jul 21 2019 *)