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A067871
Number of primes between consecutive terms of A246547 (prime powers p^k, k >= 2).
2
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, 26, 18, 0, 2, 28, 52, 36, 42, 32, 45, 45, 47, 19, 30, 106, 36, 35, 4, 114, 28, 135, 89, 42, 87, 42, 34, 66, 192, 106, 56, 23, 39, 37, 165, 49, 37, 262, 58, 160, 22
OFFSET
1,1
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 667 terms from Lei Zhou)
FORMULA
a(n) = A000720(A025475(n+3)) - A000720(A025475(n+2)) - David Wasserman, Dec 20 2002
EXAMPLE
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.
MATHEMATICA
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 *)
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Mar 07 2002
EXTENSIONS
More terms from David Wasserman, Dec 20 2002
Definition clarified by N. J. A. Sloane, Oct 27 2023
STATUS
approved