A373143 a(n) = 1 if both A003415(n) and A276085(n) are multiples of 3, otherwise 0, where A003415 is the arithmetic derivative 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, 1, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1

Offset

1

Comments

Question: Does this sequence have an asymptotic mean?

Links

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

Index entries for characteristic functions

Formula

a(n) = A359430(n) * A372573(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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)); };
A373143(n) = (!(A003415(n)%3) && !(A276085(n)%3));

Crossrefs

Characteristic function of A373144.

Cf. A003415, A276085, A359430, A372573.

Sequence in context: A156297 A373483 A373372 * A373836 A015626 A015920

Adjacent sequences: A373140 A373141 A373142 * A373144 A373145 A373146

Keyword

nonn

Author

Antti Karttunen, May 26 2024

Status

approved