login
A372573
a(n) = 1 if A276085(n) is a multiple of 3, otherwise 0, where A276085 is the primorial base log-function.
12
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).
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
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);
CROSSREFS
Characteristic function of A339746.
Cf. also A369001.
Sequence in context: A303561 A284680 A004555 * A200261 A288855 A138711
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, May 26 2024
STATUS
approved