|
|
|
|
0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
a(n) for n >= 2 equals GCD of minimal and maximal exponents in prime factorization of n. For n >= 2 holds: a(n)*A157754(n) = A051904(n)*A051903(n). a(n) for n >= 2 it deviates from A052409(n), first different term is a(10800) = a(2^4*3^3*5^2), a(10800) = gcd(2,4) = 2, A052409(10800) = gcd(2,3,4) = 1.
|
|
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).
|
|
EXAMPLE
|
For n = 12 = 2^2 * 3^1 we have a(12) = gcd(2,1) = 1.
|
|
MATHEMATICA
|
Table[GCD @@ {Min@ #, Max@ #} - Boole[n == 1] &@ FactorInteger[n][[All, -1]], {n, 100}] (* Michael De Vlieger, Jul 12 2017 *)
|
|
PROG
|
(PARI)
A051903(n) = if((1==n), 0, vecmax(factor(n)[, 2]));
A051904(n) = if((1==n), 0, vecmin(factor(n)[, 2]));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|