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

Offset: 1

Author

Giovanni Resta, Jan 10 2014

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A050765, A105779.

Programs

Mathematica

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

PARI

gpf(n)=n=factor(n)[,1];n[#n]
is(n)=nextprime(n)-n==gpf(n)+1 \\ Charles R Greathouse IV, Jan 10 2014