A363992 - OEIS

A363992

The number of ways 2n can be expressed as the sum of an odd prime number and an odd nonprime, both of which are relatively prime to n.

0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 1, 3, 3, 1, 6, 3, 1, 8, 4, 2, 6, 6, 3, 5, 7, 4, 8, 8, 2, 12, 7, 3, 13, 6, 6, 11, 9, 4, 12, 12, 4, 13, 13, 3, 14, 14, 8, 17, 11, 7, 15, 15, 10, 14, 13, 7, 16, 18, 3, 22, 18, 7, 24, 14, 11, 20, 20, 14, 17, 18, 10, 22, 22, 8

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..75.

EXAMPLE

For n=24 (2n=48), we have a(24)=3 since 48=1+47, 48=13+35, and 48=23+25. These are the only sums containing one prime and one nonprime, both of which are relatively prime to n.

MAPLE

f:= proc(n) local k;

nops(select(k -> igcd(n, k) = 1 and igcd(n, 2*n-k) = 1 and isprime(k) and not isprime(2*n-k), [seq(k, k=1..2*n-1, 2)]))

end proc:

map(f, [$0..100]); # Robert Israel, Jul 03 2023

PROG

(Sage)

def d(a):

"""

This function returns the number of ways n=2a can be expressed as the sum of one prime number and an odd composite that are relatively prime to n

"""

d=0