A080769 Number of primes between consecutive integer powers with exponent > 1.

2, 2, 0, 2, 3, 0, 2, 0, 4, 3, 4, 3, 5, 0, 1, 3, 5, 5, 3, 1, 5, 1, 7, 5, 2, 4, 6, 7, 7, 5, 2, 6, 9, 8, 7, 8, 9, 8, 8, 6, 4, 9, 10, 9, 10, 7, 2, 9, 12, 11, 12, 6, 5, 9, 12, 11, 3, 10, 8, 0, 2, 13, 15, 10, 11, 15, 7, 9, 12, 13, 11, 0, 12, 17, 2, 11, 16, 16, 13, 17, 15, 14, 16, 15, 15, 17, 13, 2, 19

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10001

Formula

a(n) = A000720(A001597(n+1)) - A000720(A001597(n)). - Jianing Song, Nov 19 2019

Example

a(1) = 2 because there are 2 primes between 1^2 and 2^2, viz., 2 and 3.
a(2) = 2 because there are 2 primes between 2^2 and 2^3, viz., 5 and 7.
a(3) = 0 because there are no primes between 2^3 and 3^2.

Mathematica

Count[#, _?PrimeQ] & /@ Range @@@ # &@ Partition[#, 2, 1] &@ Select[Range@ 5000, # == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1 &] (* Michael De Vlieger, Jun 30 2016, after Ant King at A001597 *)

Crossrefs

Cf. A001597, A053289, A000720, A000040.

Sequence in context: A278521 A195910 A240590 * A328903 A143539 A249063

Adjacent sequences: A080766 A080767 A080768 * A080770 A080771 A080772

Keyword

easy,nonn

Author

Walter Nissen, Mar 10 2003

Extensions

Offset corrected by Jianing Song, Nov 19 2019

Status

approved