OFFSET
1,8
COMMENTS
The sum of exponents larger than 2 in the prime factorization of n.
The number of distinct primes factors of the largest divisor of n that is a cubefull number is A295659(n).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Rafael Jakimczuk and Matilde LalĂn, Sums of omega(n) and Omega(n) over the k-free parts and k-full parts of some particular sequences, Integers, Vol. 22 (2022), Article #A113.
FORMULA
Additive with a(p^e) = 0 if e <= 2, and a(p^e) = e for e >= 3.
a(n) >= 0, with equality if and only if n is cubefree (A004709).
MATHEMATICA
f[p_, e_] := If[e < 3, 0, e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecsum(apply(x -> if(x < 3, 0, x), factor(n)[, 2]));
CROSSREFS
Similar sequence: A275812 (number of primes factors of the powerful part).
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 28 2023
STATUS
approved