A244508 Number of odd prime powers (A246655) between 2^n and 2^(n+1).

0, 1, 2, 3, 7, 8, 16, 25, 46, 80, 141, 263, 473, 882, 1628, 3044, 5734, 10779, 20428, 38687, 73653, 140425, 268340, 513866, 986033, 1894409, 3646134, 7027825, 13562625, 26208248, 50698865, 98184467, 190338061, 369326690, 717271793, 1394198586, 2712112561

Offset

0,3

Links

Ray Chandler, Table of n, a(n) for n = 0..91 (using b-file from A007053, corrected n = 45..52, n = 0..52 from Hiroaki Yamanouchi)

Formula

a(n) = A182908(n+1) - A182908(n). - Ray Chandler, Aug 20 2021

Example

Between 2 and 4, there is just 1 prime power: 3, so a(1) = 1.
Between 4 and 8, there are 2 prime powers: 5 and 7, so a(2) = 2.

Mathematica

Table[Count[Range[2^n + 1, 2^(n + 1) - 1], _?PrimePowerQ], {n, 0, 27}] (* Ivan N. Ianakiev, Nov 18 2014 *)

Prog

(PARI) a(n) = sum(i=2^n+1, 2^(n+1)-1, isprimepower(i)>0);

Crossrefs

Cf. A246655 (prime powers), A182908 (positions of 2^n among prime powers).

Sequence in context: A363847 A076550 A062269 * A060121 A002964 A166966

Adjacent sequences: A244505 A244506 A244507 * A244509 A244510 A244511

Keyword

nonn

Author

Michel Marcus, Nov 17 2014

Extensions

a(28)-a(36) from Hiroaki Yamanouchi, Nov 20 2014

Minor edits by Ray Chandler, Aug 20 2021

Status

approved