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A365632
The number of divisors of n that are terms of A072873.
6
1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1
OFFSET
1,4
COMMENTS
The sum of these divisors is A365633(n) and the largest of them is A327939(n).
LINKS
FORMULA
Multiplicative with a(p^e) = 1 + floor(e/p).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} p^p/(p^p-1) = 1.3850602852... .
MATHEMATICA
f[p_, e_] := 1 + Floor[e/p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + f[i, 2]\f[i, 1]); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Sep 14 2023
EXTENSIONS
Data corrected by Amiram Eldar, Sep 20 2023
STATUS
approved