OFFSET
1,4
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
Multiplicative with a(p^e) = p if e >= p, otherwise 1.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (p-1)/p^p) = 1.3443209052633459342... . - Amiram Eldar, Nov 07 2022
EXAMPLE
For n = 12 = 2^2 * 3^1, only prime factor p = 2 satisfies p^p | 12, thus a(12) = 2.
For n = 108 = 2^2 * 3^3, both prime factors p = 2 and p = 3 satisfy p^p | 108, thus a(108) = 2*3 = 6.
MATHEMATICA
Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; IntegerQ@ p :> If[e >= p, p, 1]] &, 120] (* Michael De Vlieger, Oct 01 2019 *)
PROG
(PARI) A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved