A333701 Number of ways to write n as the sum of two positive integers with the same number of distinct prime factors.

0, 1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 3, 3, 3, 5, 2, 5, 3, 6, 5, 5, 2, 7, 4, 6, 6, 7, 4, 9, 4, 10, 6, 11, 6, 12, 3, 9, 7, 11, 6, 10, 6, 10, 9, 12, 5, 14, 7, 14, 8, 12, 6, 16, 8, 15, 10, 14, 8, 18, 10, 15, 10, 16, 8, 20, 9, 18, 14, 17, 10, 23, 12, 18, 15, 17

Offset

1,6

Links

Table of n, a(n) for n=1..76.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} [omega(i) = omega(n-i)], where [] is the Iverson bracket and omega is the number of distinct prime factors of n (A001221).

Mathematica

Table[Sum[KroneckerDelta[PrimeNu[i], PrimeNu[n - i]], {i, Floor[n/2]}], {n, 100}]

Crossrefs

Cf. A001221, A333708 (distinct numbers).

Sequence in context: A024366 A218123 A288157 * A140682 A049317 A134544

Adjacent sequences: A333698 A333699 A333700 * A333702 A333703 A333704

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 02 2020

Status

approved