

A227065


The number of partitions of 2n into exactly two parts such that the smaller and larger parts are not both prime.


1



1, 1, 2, 3, 3, 5, 5, 6, 7, 8, 8, 9, 10, 12, 12, 14, 13, 14, 17, 17, 17, 19, 19, 19, 21, 23, 22, 25, 25, 24, 28, 27, 27, 32, 30, 30, 32, 33, 32, 36, 36, 34, 38, 40, 36, 42, 42, 41, 46, 44, 43, 47, 47, 46, 49, 49, 47, 52, 53, 48, 57, 57, 53, 61, 58, 57, 61, 63, 61, 63
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OFFSET

1,3


COMMENTS

Complement of A045917(n).


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Index entries for sequences related to partitions


FORMULA

a(n) = n  A045917(n).


MAPLE

A227065 := proc(n)
nA045917(n) ;
end proc:
seq(A227065(n), n=1..100) ; # R. J. Mathar, Jul 01 2013


MATHEMATICA

Table[n  Sum[(PrimePi[2 n  i]  PrimePi[2 n  i  1]) (PrimePi[i]  PrimePi[i  1]), {i, n}], {n, 100}] (* Wesley Ivan Hurt, Apr 07 2018 *)
f[n_]:=Length[Select[2 n  Prime[Range[PrimePi[n]]], PrimeQ]]; Table[n  f[n], {n, 100}] (* Vincenzo Librandi, Apr 10 2018 *)


CROSSREFS

Cf. A045917.
Sequence in context: A023816 A159237 A335599 * A010761 A320840 A161172
Adjacent sequences: A227062 A227063 A227064 * A227066 A227067 A227068


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Jun 30 2013


STATUS

approved



