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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 (list; graph; refs; listen; history; text; internal format)
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)

    n-A045917(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

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)