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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.
2
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
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.
Sequence in context: A267679 A267868 A374043 * A288733 A095111 A166253
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 26 2024
STATUS
approved