A235425 - OEIS

%I #10 Jul 14 2021 07:47:31

%S 8,64,128,625,729,1701,2625,3025,4096,6435,8505,10115,12675,14641,

%T 17303,19343,19683,19845,21125,25515,25725,26325,26741,27783,32768,

%U 33075,33275,34075,35721,38025,39375,42525,43875,50193,59319,60835,61731,70805,75411,75803

%N 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.

%H Giovanni Resta, <a href="/A235425/b235425.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

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

%o is(n)=nextprime(n)-n==gpf(n)+1 \\ _Charles R Greathouse IV_, Jan 10 2014

%Y Cf. A050765, A105779.

%K nonn

%O 1,1

%A _Giovanni Resta_, Jan 10 2014