OFFSET
1,4
COMMENTS
LINKS
FORMULA
a(1) = 0, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = k, for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k > 2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1) k = natural numbers (A000027).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A033150. - Amiram Eldar, Sep 11 2024
EXAMPLE
For n = 12 = 2^2 * 3^1 we have a(12) = lcm(2,1) = 2.
For n = 144 = 2^4 * 3^2 we have a(144) = lcm(4,2) = 4.
MATHEMATICA
Table[LCM @@ {Min@ #, Max@ #} - Boole[n == 1] &@ FactorInteger[n][[All, -1]], {n, 100}] (* Michael De Vlieger, Jul 12 2017 *)
PROG
(PARI) a(n) = if(n == 1, 0, my(e = factor(n)[, 2]); lcm(vecmin(e), vecmax(e))); \\ Amiram Eldar, Sep 11 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 05 2009
STATUS
approved