A333708 Number of ways to write n as the sum of two distinct positive integers with the same number of distinct prime factors.

0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 3, 3, 3, 2, 3, 4, 2, 4, 3, 5, 5, 4, 2, 6, 4, 5, 6, 6, 4, 8, 4, 9, 6, 10, 6, 11, 3, 8, 7, 10, 6, 9, 6, 9, 9, 11, 5, 13, 7, 13, 8, 11, 6, 15, 8, 14, 10, 13, 8, 17, 10, 14, 10, 15, 8, 19, 9, 17, 14, 16, 10, 22, 12, 17, 15, 16, 12

Offset

1,7

Links

Table of n, a(n) for n=1..77.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor((n-1)/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 - 1)/2]}], {n, 100}]

Crossrefs

Cf. A001221 (omega), A333701.

Sequence in context: A308174 A126237 A243164 * A132203 A158925 A262868

Adjacent sequences: A333705 A333706 A333707 * A333709 A333710 A333711

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 02 2020

Status

approved