A235425 - OEIS

A235425

Numbers k such that between k and the next prime there are gpf(k) numbers, where gpf(k) denotes the largest prime factor of k.

8, 64, 128, 625, 729, 1701, 2625, 3025, 4096, 6435, 8505, 10115, 12675, 14641, 17303, 19343, 19683, 19845, 21125, 25515, 25725, 26325, 26741, 27783, 32768, 33075, 33275, 34075, 35721, 38025, 39375, 42525, 43875, 50193, 59319, 60835, 61731, 70805, 75411, 75803

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

EXAMPLE

64 = 2^6, whose largest prime factor is 2, is in the sequence because between 64 and 67 (the next prime) there are 2 numbers, 65 and 66.

MATHEMATICA

Select[Range[10^5], NextPrime[#] - # == 1 + FactorInteger[#][[-1, 1]] &]

PROG

(PARI) gpf(n)=n=factor(n)[, 1]; n[#n]

is(n)=nextprime(n)-n==gpf(n)+1 \\ Charles R Greathouse IV, Jan 10 2014