

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
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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



