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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 Antti Karttunen, Table of n, a(n) for n = 1..65537 Index entries for characteristic functions. Index entries for sequences computed from exponents in factorization of n. 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. Cf. A008966, A181819, A327498, A327499. Sequence in context: A142720 A196308 A091862 * A237048 A344880 A167020 Adjacent sequences: A351561 A351562 A351563 * A351565 A351566 A351567 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.)