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

1,1

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

Crossrefs

Cf. A050765, A105779.

Sequence in context: A116978 A125110 A209990 * A255932 A043152 A044195

Adjacent sequences: A235422 A235423 A235424 * A235426 A235427 A235428

Keyword

nonn

Author

Giovanni Resta, Jan 10 2014

Status

approved