

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

Table of n, a(n) for n=1..70.
Index entries for sequences related to Goldbach conjecture
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{i=1..floor((n1)/2)} 1  A010051(i)*A010051(ni).


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



