A269769 Numbers of the form p^k - k where p is a prime number and k > 1.
2, 5, 7, 12, 23, 24, 27, 47, 58, 77, 119, 121, 122, 167, 238, 248, 287, 340, 359, 503, 527, 621, 723, 839, 959, 1014, 1328, 1367, 1679, 1847, 2037, 2180, 2194, 2207, 2397, 2807, 3120, 3479, 3719, 4084, 4487, 4910, 5039, 5327, 6239, 6553, 6856, 6887, 7919, 8179
Offset: 1
Keywords
Examples
2 is a term because 2 = 2^2 - 2.
5 is a term because 5 = 2^3 - 3.
7 is a term because 7 = 3^2 - 2.
12 is a term because 12 = 2^4 - 4.
121 is a term because 121 = 2^7 - 7.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
N:= 10000: # to get all terms <= N P:= select(isprime, [$1..floor((N+2)^(1/2))]): S:= {}: for k from 2 do pmax:= floor((N+k)^(1/k)); if pmax < 2 then break fi; S:= S union {seq(p^k-k, p = select(`<=`,P,pmax))}; od: sort(convert(S,list)); # Robert Israel, Mar 21 2017
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