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A351564 a(n) = 1 if all the exponents in the prime factorization of n are distinct, and 0 otherwise. 7
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
LINKS
FORMULA
a(n) = A008966(A181819(n)).
EXAMPLE
For n = 4 = 2^2, all the exponents present [2] are distinct, therefore a(4) = 1.
For n = 300 = 2^2 * 3^1 * 5^2, the exponents are [2, 1, 2], thus they are not all distinct, therefore a(300) = 0.
MATHEMATICA
a[n_] := If[UnsameQ @@ FactorInteger[n][[;; , 2]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 30 2022 *)
PROG
(PARI) A351564(n) = issquarefree(factorback(apply(e->prime(e), (factor(n)[, 2]))));
CROSSREFS
Characteristic function of A130091.
Sequence in context: A142720 A196308 A091862 * A237048 A344880 A167020
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 02 2022
STATUS
approved

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Last modified June 22 15:32 EDT 2024. Contains 373587 sequences. (Running on oeis4.)