A067871 - OEIS

%I #19 Oct 27 2023 11:12:08

%S 2,0,2,3,0,2,4,3,4,8,0,1,8,14,1,7,7,4,25,2,15,15,17,16,10,45,2,44,20,

%T 26,18,0,2,28,52,36,42,32,45,45,47,19,30,106,36,35,4,114,28,135,89,42,

%U 87,42,34,66,192,106,56,23,39,37,165,49,37,262,58,160,22

%N Number of primes between consecutive terms of A246547 (prime powers p^k, k >= 2).

%H Michael De Vlieger, <a href="/A067871/b067871.txt">Table of n, a(n) for n = 1..10000</a> (first 667 terms from Lei Zhou)

%F a(n) = A000720(A025475(n+3)) - A000720(A025475(n+2)) - _David Wasserman_, Dec 20 2002

%e The first few prime powers A246547 are 4, 8, 9, 16. The first few primes are 2, 3, 5, 7, 11, 13. We have (4), 5, 7, (8), (9), 11, 13, (16) and so the sequence begins with 2, 0, 2.

%t t = {}; cnt = 0; Do[If[PrimePowerQ[n], If[FactorInteger[n][[1, 2]] == 1, cnt++, AppendTo[t, cnt]; cnt = 0]], {n, 4 + 1, 30000}]; t (* _T. D. Noe_, May 21 2013 *)

%t nn = 2^20; Differences@ Map[PrimePi, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], PrimePowerQ] ] ] (* _Michael De Vlieger_, Oct 26 2023 *)

%Y Cf. A000040, A246547, A246655.

%K nonn,easy

%O 1,1

%A _Jon Perry_, Mar 07 2002

%E More terms from _David Wasserman_, Dec 20 2002

%E Definition clarified by _N. J. A. Sloane_, Oct 27 2023