A374041 a(n) = 1 if A276085(n) and A328768(n) are both multiples of 3, otherwise 0, where A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.

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

Offset

1

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) = A372573(n) * A373991(n).

a(n) = A372573(n) * [A007949(n) != 1], where [ ] is the Iverson bracket.

a(n) = A079978(A374031(n)).

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)); };
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i, 1])-1)/f[i, 1]));
A374041(n) = (!(A276085(n)%3) && !(A328768(n)%3));
(PARI) A374041(n) = { my(v2 = valuation(n, 2), v3 = valuation(n, 3)); ((v3 != 1) && 0==((v2-v3)%3)); };

Crossrefs

Characteristic function of A374042.

Cf. A002110, A079978, A276085, A328768, A372573, A373991, A374031.

Sequence in context: A267679 A267868 A374043 * A288733 A095111 A166253

Adjacent sequences: A374038 A374039 A374040 * A374042 A374043 A374044

Keyword

nonn

Author

Antti Karttunen, Jun 26 2024

Status

approved