A372574 a(n) = 1 if the squarefree part of n is congruent to 1 or 5 modulo 6, otherwise 0.

1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1

Offset

1

Comments

a(n) = 1 iff A007913(n) is in A007310.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

a(n) = A354354(A007913(n)).

Sum_{k=1..n} a(k) ~ n/2. - Amiram Eldar, May 27 2024

Multiplicative with a(p^e) = [e == 0 (mod 2)] if p <= 3 and a(p^e) = 1 if p > 3, where [ ] is the Iverson bracket.

Mathematica

a[n_] := If[And @@ EvenQ[IntegerExponent[n, {2, 3}]], 1, 0]; Array[a, 100] (* Amiram Eldar, May 27 2024 *)

Prog

(PARI) A372574(n) = (1==gcd(core(n), 6));
(PARI) A372574(n) = { my(f = factor(n)); prod(k=1, #f~, if(f[k, 1]<=3, !(f[k, 2]%2), 1)); }; \\ Antti Karttunen, May 29 2024

Crossrefs

Characteristic function of A339690.

Cf. A007310, A007913, A354354.

Sequence in context: A373155 A078650 A285305 * A028863 A089012 A083035

Adjacent sequences: A372571 A372572 A372573 * A372575 A372576 A372577

Keyword

nonn,mult,easy

Author

Antti Karttunen, May 26 2024

Status

approved