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A339708 a(n) is the number of decompositions of 2*n as the sum of an odd prime and a semiprime. 2
0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 1, 3, 4, 1, 4, 2, 2, 6, 4, 3, 5, 5, 2, 4, 7, 4, 7, 6, 3, 10, 5, 4, 10, 6, 6, 7, 8, 5, 9, 9, 4, 8, 10, 4, 11, 10, 9, 13, 9, 7, 10, 10, 9, 10, 9, 8, 11, 13, 4, 16, 13, 9, 15, 11, 11, 13, 14, 13, 13, 10, 10, 15, 16, 8, 19, 11, 11, 17, 14, 15, 17, 18, 9, 13, 17, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

Robert Israel, Table of n, a(n) for n = 1..5000

EXAMPLE

a(10) = 2 because 20 = 5+15 = 11+9 where 5 and 11 are primes and 15 and 9 are semiprimes.

MAPLE

N:= 300: # for a(1)..a(N/2)

P:= select(isprime, [seq(i, i=3..N, 2)]):

S:= sort(select(`<`, [seq(seq(P[i]*P[j], i=1..j), j=1..nops(P))], N)):

V:= Vector(N):

for p in P do

for s in S do

  v:= p+s;

    if v>N then break fi;

  V[v]:= V[v]+1

od od:

seq(V[i], i=2..N, 2);

MATHEMATICA

{0}~Join~Array[Count[IntegerPartitions[2 #, {2}, All, -(# - 2)], _?(And[AnyTrue[#, PrimeQ], AnyTrue[#, PrimeOmega[#] == 2 &]] &)] &, 86, 2] (* Michael De Vlieger, Dec 13 2020 *)

PROG

(PARI) a(n) = {my(nb=0); forprime(p=3, 2*n, if (bigomega(2*n-p) == 2, nb++); ); nb; } \\ Michel Marcus, Dec 14 2020

CROSSREFS

Cf. A001358, A235645, A339709.

Sequence in context: A076019 A071453 A212306 * A080242 A183927 A035317

Adjacent sequences:  A339705 A339706 A339707 * A339709 A339710 A339711

KEYWORD

nonn,look

AUTHOR

J. M. Bergot and Robert Israel, Dec 13 2020

STATUS

approved

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Last modified April 14 19:06 EDT 2021. Contains 342951 sequences. (Running on oeis4.)