

A334208


Number of partitions of 2n into two composite parts, (r,s), such that r and s have the same number of primes less than or equal to them.


0



0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0
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OFFSET

1,9


COMMENTS

Apparently a(n) = A051699(n) for n>=2.  R. J. Mathar, Apr 22 2020


LINKS

Table of n, a(n) for n=1..89.
Index entries for sequences related to partitions


FORMULA

a(n) = Sum_{i=2..n} [pi(i) = pi(2*ni)] * (1  c(i)) * (1  c(2*ni)), where [] is the Iverson bracket, pi is the prime counting function (A000720), and c is the prime characteristic (A010051).


EXAMPLE

a(9) = 2; 2*9 = 18 has two partitions into composite parts, (10,8) and (9,9), such that pi(10) = 4 = pi(8) and pi(9) = 4 = pi(9).


MATHEMATICA

Table[Sum[KroneckerDelta[PrimePi[i], PrimePi[2 n  i]] (1  PrimePi[i] + PrimePi[i  1]) (1  PrimePi[2 n  i] + PrimePi[2 n  i  1]), {i, 2, n}], {n, 100}]


CROSSREFS

Cf. A000720, A010051, A051699.
Sequence in context: A175599 A179759 A257260 * A159195 A265859 A271420
Adjacent sequences: A334205 A334206 A334207 * A334209 A334210 A334211


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Apr 18 2020


STATUS

approved



