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A368915
a(n) = 1 if there is no prime p such that p^p divides the arithmetic derivative of n, and 0 otherwise.
9
0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1
OFFSET
1
COMMENTS
Question: What is the asymptotic mean of this sequence (and its complement A341996)? Knowing the value for A360111 would solve this. See also related sequences like A354874 and A368916.
FORMULA
a(1) = 0; for n > 1, a(n) = A359550(A003415(n)).
For all n > 1, a(n) = 1 - A341996(n) = A359550(n) - A360111(n).
For all n > 1, A359550(n) >= a(n) >= A328308(n).
For all n >= 1, a(n) >= A354874(n).
a(n) = A368914(n) - A368913(n).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };
A368915(n) = ((n>1)&&A359550(A003415(n)));
CROSSREFS
Characteristic function of A358215.
Cf. A003415, A328308, A341996 (one's complement), A354874, A359550, A360111, A368913, A368914, A368916 [= a(A276086(n))].
Sequence in context: A284929 A286746 A155897 * A144610 A188068 A181632
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 09 2024
STATUS
approved