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A333708 Number of ways to write n as the sum of two distinct positive integers with the same number of distinct prime factors. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 12:54 EDT 2021. Contains 347598 sequences. (Running on oeis4.)