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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 (list; graph; refs; listen; history; text; internal format)
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*n-i)] * (1 - c(i)) * (1 - c(2*n-i)), 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

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)