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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: A353714 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 December 4 15:37 EST 2024. Contains 378413 sequences.
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