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A368336
The number of divisors of the largest term of A072873 that divides of n.
3
1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1
OFFSET
1,4
LINKS
FORMULA
a(n) = A000005(A327939(n)).
Multiplicative with a(p^e) = e - (e mod p) + 1.
a(n) >= 1, with equality if and only if n is in A048103.
a(n) <= A000005(n), with equality if and only if n is in A072873.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + p/(p^p-1)) = 1.86196549645040699446... .
MATHEMATICA
f[p_, e_] := (e - Mod[e, p] + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 2] - f[i, 2]%f[i, 1] + 1); }
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 21 2023
STATUS
approved