A372573 a(n) = 1 if A276085(n) is a multiple of 3, otherwise 0, where A276085 is the primorial base log-function.

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

Offset

1

Comments

a(n) = 1 iff n is of the form 2^i * 3^j * k, with k in A007310 [i.e., gcd(k, 6) = 1], and i == j (mod 3).

Links

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

Index entries for characteristic functions.

Index entries for sequences related to primorial numbers.

Formula

a(n) = [A276085(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

Sum_{k=1..n} a(k) ~ (43/91) * n. - Amiram Eldar, May 29 2024

a(n) = [A007814(n) == A007949(n) (mod 3)]. - Antti Karttunen, Nov 27 2024

Mathematica

a[n_] :=  If[Divisible[Differences[IntegerExponent[n, {2, 3}]][[1]], 3], 1, 0]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A372573(n) = !(A276085(n)%3);
(PARI) A372573(n) = !((valuation(n, 2)-valuation(n, 3))%3);

Crossrefs

Characteristic function of A339746.

Cf. A002110, A007310, A007814, A007949, A276085, A378443 (inverse Möbius transform).

Cf. also A369001.

Sequence in context: A303561 A284680 A004555 * A200261 A288855 A138711

Adjacent sequences: A372570 A372571 A372572 * A372574 A372575 A372576

Keyword

nonn,easy

Author

Antti Karttunen, May 26 2024

Status

approved