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A333701
Number of ways to write n as the sum of two positive integers with the same number of distinct prime factors.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 02 2020
STATUS
approved