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A295316 a(n) = 1 if there are no even exponents in the prime factorization of n, 0 otherwise. 6
1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Characteristic function for A268335.

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

Multiplicative with a(p^e) = A000035(e).

a(1) = 1, for n > 1, a(n) = A000035(A067029(n)) * a(A028234(n)).

a(n) = 1 iff A162641(n) = 0.

For n > 1, a(n) = A267115(n) mod 2.

MATHEMATICA

Array[Boole[AllTrue[FactorInteger[#][[All, -1]], OddQ]] &, 120] (* Michael De Vlieger, Nov 23 2017 *)

PROG

(PARI)

vecproduct(v) = { my(m=1); for(i=1, #v, m *= v[i]); m; };

A295316(n) = vecproduct(apply(e -> (e%2), factorint(n)[, 2]));

(Scheme, with memoization-macro definec)

(definec (A295316 n) (if (= 1 n) n (if (even? (A067029 n)) 0 (A295316 (A028234 n)))))

CROSSREFS

Cf. A000035, A072587 (positions of zeros), A268335 (of ones), A162641, A267115.

Cf. also A033634, A293449.

Sequence in context: A267773 A325321 A255887 * A014677 A307425 A210826

Adjacent sequences:  A295313 A295314 A295315 * A295317 A295318 A295319

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Nov 23 2017

STATUS

approved

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)