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A302479
Number of partitions of n into two distinct nonprime parts.
11
0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 5, 3, 5, 4, 6, 4, 6, 5, 7, 6, 6, 6, 9, 6, 10, 7, 8, 8, 10, 8, 11, 9, 10, 9, 12, 9, 13, 10, 13, 10, 13, 11, 15, 12, 14, 12, 16, 13, 18, 14, 15, 14, 18, 14, 20, 15, 16, 16, 20, 16, 21, 17, 20, 17
OFFSET
1,10
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} (1 - c(i)) * (1 - c(n-i)), where c = A010051.
For n > 0, a(n) = A358638(n) - A005171(n). - Antti Karttunen, Nov 25 2022
EXAMPLE
a(16) = 3; 16 = 15+1 = 12+4 = 10+6, which are distinct nonprimes.
MATHEMATICA
Table[Sum[(1 - PrimePi[n - i] + PrimePi[n - i - 1]) (1 - PrimePi[i] + PrimePi[i - 1]), {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Length[Select[IntegerPartitions[n, {2}], Length[Union[#]]==2&&Boole[PrimeQ[#]]=={0, 0}&]], {n, 80}] (* Harvey P. Dale, Dec 28 2023 *)
PROG
(PARI) A302479(n) = sum(k=1, (n-1)\2, !(isprime(k)+isprime(n-k))); \\ Antti Karttunen, Nov 25 2022
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 08 2018
STATUS
approved