%I #8 Aug 20 2024 09:14:33

%S 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,

%T 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,

%U 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

%N The maximum exponent in the prime factorization of the largest 5-smooth divisor of n.

%H Amiram Eldar, <a href="/A375536/b375536.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = A051903(A355582(n)).

%F a(n) = max(A007814(n), A007949(n), A112765(n)).

%F a(n) = 0 if and only if n is a 7-rough number (A007775).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A375538(3)/A375539(3) = 51227/36540 = 1.401943076...

%t a[n_] := Max[IntegerExponent[n, {2, 3, 5}]]; Array[a, 100]

%o (PARI) a(n) = max(max(valuation(n, 2), valuation(n, 3)), valuation(n, 5));

%Y Cf. A007775, A051903, A244417 (3-smooth analog), A355582, A375537, A375538, A375539.

%Y Cf. A007814, A007949, A112765.

%K nonn,easy

%O 1,4

%A _Amiram Eldar_, Aug 19 2024