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A369006
a(n) = 1 if there is no prime p such that p^p divides n' / gcd(n,n'), and 0 otherwise, where n' stands for the arithmetic derivative of n, A003415(n).
2
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1
OFFSET
1
COMMENTS
Question: Is there a formula for the asymptotic mean, which seems to be around 0.813...? Consider A369004 and A369007.
FORMULA
a(1) = 0, for n > 1, a(n) = A359550(A083345(n)).
A368914(n) <= a(n) <= 1 - A369004(n).
PROG
(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
A369006(n) = if(1==n, 0, A359550(A083345(n)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 14 2024
STATUS
approved