A368336 The number of divisors of the largest term of A072873 that divides of n.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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); }

Crossrefs

Cf. A000005, A048103, A072873, A327939, A365632, A368331, A368335.

Sequence in context: A176563 A093148 A069292 * A365633 A091842 A306346

Adjacent sequences: A368333 A368334 A368335 * A368337 A368338 A368339

Keyword

nonn,easy,mult

Author

Amiram Eldar, Dec 21 2023

Status

approved