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 A295630 Number of partitions of n into two distinct parts that are not both prime. 0
 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 5, 5, 6, 5, 8, 6, 8, 7, 9, 8, 11, 8, 11, 10, 13, 11, 14, 11, 14, 13, 15, 13, 17, 13, 18, 17, 18, 16, 20, 16, 20, 18, 21, 19, 23, 18, 23, 20, 25, 22, 26, 21, 26, 24, 28, 25, 29, 23, 29, 28, 30, 26, 32, 26, 33, 31, 33, 29 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS FORMULA a(n) = Sum_{i=1..floor((n-1)/2)} 1 - A010051(i)*A010051(n-i). EXAMPLE a(12) = 4; The partitions of 12 into two distinct parts are (11,1), (10,2), (9,3), (8,4) and (7,5). Of these partitions, the parts in (11,1), (10,2), (9,3) and (8,4) are not both prime, so a(12) = 4. MATHEMATICA Table[Sum[1 - (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 80}] CROSSREFS Cf. A010051, A295629. Sequence in context: A248972 A077563 A055256 * A029147 A228571 A224908 Adjacent sequences:  A295627 A295628 A295629 * A295631 A295632 A295633 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Nov 24 2017 STATUS approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)