

A294602


a(n) = pi(n1)  pi(floor(n/2)), where pi is A000720.


2



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
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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((n1)/2)} A010051(ni).  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](n1)numtheory[pi](floor(n/2)) ;
end proc:
seq(A294602(n), n=1..120) ; # R. J. Mathar, Dec 17 2017


MATHEMATICA

Array[PrimePi[#  1]  PrimePi[Floor[#/2]] &, 86] (* Michael De Vlieger, Nov 03 2017 *)


PROG

(MAGMA) [0, 0] cat [#PrimesInInterval(Floor(n/2)+1, n1): n in [3..86]];
(PARI) vector(86, n, primepi(n1)primepi(n\2))


CROSSREFS

Cf. A000720, A001221, A010051, A056171.
Sequence in context: A198337 A206483 A087011 * A000174 A156268 A053257
Adjacent sequences: A294599 A294600 A294601 * A294603 A294604 A294605


KEYWORD

nonn,easy


AUTHOR

Arkadiusz Wesolowski, Nov 03 2017


STATUS

approved



