OFFSET
0,5
FORMULA
EXAMPLE
a(5) = 7; Since 5 can be expressed in one way as the sum of the two primes 2 and 3, we add the sum of their divisors separately: sigma(2) + sigma(3) = 3 + 4 = 7.
a(10) = 24; Since 10 can be expressed in two ways as the sum of two primes, we add the sum of the divisors of each prime p and q: 10 = 3+7 = 5+5, so sigma(3) + sigma(7) + sigma(5) + sigma(5) = 4 + 8 + 6 + 6 = 24.
MAPLE
MATHEMATICA
Table[(n+2) Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, 2, Floor[n/2]}], {n, 0, 80}]
PROG
(PARI) a(n) = sum(i=0, n\2, if (isprime(i) && isprime(n-i), sigma(i)+sigma(n-i))); \\ Michel Marcus, Mar 05 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 05 2016
STATUS
approved