

A338776


a(n) = card(GB(2*n)), where GB(n) is the set of primes which are Goldbachassociated with n.


2



0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 4, 2, 3, 5, 2, 3, 4, 1, 4, 5, 3, 3, 5, 3, 4, 7, 3, 3, 8, 3, 4, 6, 3, 5, 7, 3, 4, 6, 4, 5, 8, 4, 5, 11, 4, 4, 10, 3, 6, 8, 4, 4, 6, 6, 5, 9, 5, 4, 11, 3, 6, 9, 4, 6, 8, 4, 5, 11
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OFFSET

0,10


COMMENTS

For an integer n >= 0 we say a prime p is gbassociated with n if sqrt(n) < p <= n/2 and no prime q which is <= sqrt(n) divides p*(p  n). Let GB(n) be the set of integers which are gbassociated with n (for examples see A338777). a(n) is the number of primes which are gbassociated with n.
If a(n) > 0 for n >= 3 then Goldbach's conjecture is true.


LINKS

Peter Luschny, Table of n, a(n) for n = 0..1000


FORMULA

a(n) <= A002375(n).
a(n) = A002375(n) <=> n in A244408 (for n >= 2).


EXAMPLE

Comparison of the sets whose cardinality is given by A002375(n) resp. a(n).
m A002375 A338776
32 [29, 19] [19]
34 [31, 29, 23, 17] [23, 17]
36 [31, 29, 23, 19] [29, 23, 19]
38 [31, 19] [31, 19]


PROG

(SageMath) # [using gb_associated from A338777]
def A338776(n):
return len(gb_associated(2*n))
print([A338776(n) for n in range(87)])


CROSSREFS

Cf. A338777, A002375, A244408.
Sequence in context: A248218 A182110 A175328 * A198325 A293909 A002850
Adjacent sequences: A338773 A338774 A338775 * A338777 A338778 A338779


KEYWORD

nonn


AUTHOR

Peter Luschny, Nov 08 2020


STATUS

approved



