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

1,7

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).

Links

Table of n, a(n) for n=1..74.

Example

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

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 *)

Crossrefs

Cf. A277624.

Sequence in context: A130855 A235963 A100196 * A094708 A302931 A227145

Adjacent sequences: A278075 A278076 A278077 * A278079 A278080 A278081

Keyword

nonn

Author

Peter Luschny, Dec 28 2016

Status

approved