A373372 a(n) = 1 if A001414(n) and A276085(n) are both multiples of 3, otherwise 0, where A001414 is the sum of prime factors with repetition and A276085 is the primorial base log-function.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = A373371(n) * A372573(n).

a(n) = [A373362(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

Prog

(PARI)
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
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)); };
A373372(n) = (!(A001414(n)%3) && !(A276085(n)%3));

Crossrefs

Characteristic function of A373373.

Cf. A001414, A276086, A372573, A373362, A373371.

Cf. also A373143.

Sequence in context: A240332 A156297 A373483 * A373143 A373836 A015626

Adjacent sequences: A373369 A373370 A373371 * A373373 A373374 A373375

Keyword

nonn

Author

Antti Karttunen, Jun 02 2024

Status

approved