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A356310
a(n) = 1 if A003415(n) and A276086(n) are relatively prime, otherwise 0. Here A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
5
1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1
OFFSET
0
FORMULA
a(n) = [1 == A327858(n)], where [ ] is the Iverson bracket.
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356310(n) = (1==gcd(A003415(n), A276086(n)));
CROSSREFS
Characteristic function of A356311, whose complement A356312 gives the positions of 0's.
Cf. also A356162.
Sequence in context: A129565 A225145 A121967 * A285430 A284368 A287725
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 03 2022
STATUS
approved