This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A067871 #27 Jun 03 2025 01:09:20
%S A067871 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 A067871 26,18,0,2,28,52,36,42,32,45,45,47,19,30,106,36,35,4,114,28,135,89,42,
%U A067871 87,42,34,66,192,106,56,23,39,37,165,49,37,262,58,160,22
%N A067871 Number of primes between consecutive terms of A246547 (prime powers p^k, k >= 2).
%C A067871 Does this sequence have any terms appearing infinitely often? In particular, are {2, 5, 11, 32, 77} the only zeros? As an example, {121, 122, 123, 124, 125} is an interval containing no primes, corresponding to a(11) = 0. - _Gus Wiseman_, Dec 02 2024
%H A067871 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 A067871 a(n) = A000720(A025475(n+3)) - A000720(A025475(n+2)). - _David Wasserman_, Dec 20 2002
%e A067871 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.
%e A067871 The initial terms count the following sets of primes: {5,7}, {}, {11,13}, {17,19,23}, {}, {29,31}, {37,41,43,47}, ... - _Gus Wiseman_, Dec 02 2024
%t A067871 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 A067871 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 A067871 For primes between nonsquarefree numbers we have A236575.
%Y A067871 For composite instead of prime we have A378456.
%Y A067871 A000015 gives the least prime power >= n.
%Y A067871 A000040 lists the primes, differences A001223.
%Y A067871 A000961 lists the powers of primes, differences A057820.
%Y A067871 A080101 counts prime powers between primes.
%Y A067871 A246547 lists the non prime prime powers, differences A053707.
%Y A067871 A246655 lists the prime powers not including 1, complement A361102.
%Y A067871 Cf. A001597, A024619, A031218, A046933, A276781, A345531, A366833, A377051, A377057, A377282, A377286-A377288.
%K A067871 nonn,easy
%O A067871 1,1
%A A067871 _Jon Perry_, Mar 07 2002
%E A067871 More terms from _David Wasserman_, Dec 20 2002
%E A067871 Definition clarified by _N. J. A. Sloane_, Oct 27 2023