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A067871 Number of primes between consecutive prime powers. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Lei Zhou, Table of n, a(n) for n = 1..667

FORMULA

a(n) = A000720(A025475(n+3)) - A000720(A025475(n+2)) - David Wasserman, Dec 20 2002

EXAMPLE

The first few prime powers 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 *)

CROSSREFS

Sequence in context: A127710 A137510 A247303 * A198632 A060155 A209127

Adjacent sequences:  A067868 A067869 A067870 * A067872 A067873 A067874

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Mar 07 2002

EXTENSIONS

More terms from David Wasserman, Dec 20 2002

STATUS

approved

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)