login
A375536
The maximum exponent in the prime factorization of the largest 5-smooth divisor of n.
3
0, 1, 1, 2, 1, 1, 0, 3, 2, 1, 0, 2, 0, 1, 1, 4, 0, 2, 0, 2, 1, 1, 0, 3, 2, 1, 3, 2, 0, 1, 0, 5, 1, 1, 1, 2, 0, 1, 1, 3, 0, 1, 0, 2, 2, 1, 0, 4, 0, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 2, 0, 1, 2, 6, 1, 1, 0, 2, 1, 1, 0, 3, 0, 1, 2, 2, 0, 1, 0, 4, 4, 1, 0, 2, 1, 1, 1, 3, 0, 2, 0, 2, 1, 1, 1, 5, 0, 1, 2, 2, 0, 1, 0, 3, 1
OFFSET
1,4
FORMULA
a(n) = A051903(A355582(n)).
a(n) = max(A007814(n), A007949(n), A112765(n)).
a(n) = 0 if and only if n is a 7-rough number (A007775).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A375538(3)/A375539(3) = 51227/36540 = 1.401943076...
MATHEMATICA
a[n_] := Max[IntegerExponent[n, {2, 3, 5}]]; Array[a, 100]
PROG
(PARI) a(n) = max(max(valuation(n, 2), valuation(n, 3)), valuation(n, 5));
CROSSREFS
Cf. A007775, A051903, A244417 (3-smooth analog), A355582, A375537, A375538, A375539.
Sequence in context: A085144 A156578 A171846 * A097230 A144789 A285097
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 19 2024
STATUS
approved