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A362831
Number of partitions of n into two distinct parts (s,t) such that pi(s) = pi(t).
1
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1
OFFSET
1,17
FORMULA
a(n) = Sum_{k=1..floor((n-1)/2)} [pi(k) = pi(n-k)], where [ ] is the Iverson bracket and pi is the prime counting function (A000720).
a(n) = (A362721(n-1) - ((n-1) mod 2))/2.
EXAMPLE
a(51) = 3. The 3 partitions of 51 are (23,28), (24,27), and (25,26).
MATHEMATICA
Table[Sum[KroneckerDelta[PrimePi[k], PrimePi[n - k]], {k, Floor[(n - 1)/2]}], {n, 100}]
CROSSREFS
Cf. A000720 (pi), A362721.
Sequence in context: A338971 A244600 A288558 * A269241 A086013 A340671
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 04 2023
STATUS
approved