A254033 Number of primes dividing exactly one number in the next largest gap between primes.

0, 1, 2, 3, 6, 10, 15, 20, 21, 28, 37, 44, 53, 76, 96, 113, 123, 135, 142, 150, 181, 191, 235, 270, 291, 294, 313, 327, 334, 395, 403, 411, 445, 478, 496, 539, 582, 587, 654, 693, 722, 732, 757, 754, 772, 778, 791, 832, 830, 848, 920, 930, 955, 1004, 1053, 1151, 1240

Offset: 1

Author

Mamuka Jibladze, Jan 23 2015

Keywords

• nonn

Examples

			The 5th largest prime gap (after 2-3, 3-5, 7-11 and 23-29) occurs between 89 and 97, and there are 6 primes which occur exactly once in this gap, namely 7 (dividing 91), 13 (dividing 91), 19 (dividing 95), 23 (dividing 92), 31 (dividing 93) and 47 (dividing 94), so a(5)=6.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..75

Crossrefs

Sequences related to increasing prime gaps: A005250, A002386, A000101, A005669.

Programs

Mathematica

gp = (* the list of primes in A002386 *); f[n_] := Block[{p = gp[[n]], q = NextPrime[ gp[[n]]]}, r = Range[p + 1, q - 1]; lng = Length@ r; t = Split@ Sort@ Flatten@ Table[ First@# & /@ FactorInteger[ r[[i]]], {i, lng}]; Length@ Select[t, Length@# == 1 &]]; Array[f, 75] (* Robert G. Wilson v, Jan 23 2015 *)

Extensions

a(43)-a(57) from Robert G. Wilson v, Jan 23 2015