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A327936
Multiplicative with a(p^e) = p if e >= p, otherwise 1.
21
1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2
OFFSET
1,4
LINKS
FORMULA
Multiplicative with a(p^e) = p if e >= p, otherwise 1.
A001221(a(n)) = A129251(n).
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
Differs from A129252 for the first time at n=108.
Sequence in context: A081117 A368334 A129252 * A333748 A022929 A307706
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved