A294602 - OEIS

A294602

a(n) = pi(n-1) - pi(floor(n/2)), where pi is A000720.

0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 9, 9, 10, 10, 9

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,8

COMMENTS

Number of primes in the interval (n/2, n).

Number of primes among the larger parts of the partitions of n into two distinct parts. For n=8, the partitions of 8 into two distinct parts are (7,1), (6,2), (5,3); 7 and 5 are prime so a(8) = 2. - Wesley Ivan Hurt, Apr 07 2018

LINKS

Table of n, a(n) for n=1..86.

FORMULA

a(n) = A056171(n) - A010051(n).

a(n) = Sum_{i=1..floor((n-1)/2)} A010051(n-i). - Wesley Ivan Hurt, Apr 07 2018

EXAMPLE

a(8) = 2 because there are 2 primes between 4 and 8: 5, 7.

a(19) = 3 because there are 3 primes between 9 and 19: 11, 13, 17.

MAPLE

A294602 := proc(n)

numtheory[pi](n-1)-numtheory[pi](floor(n/2)) ;

end proc: