A368915 - OEIS

A368915

a(n) = 1 if there is no prime p such that p^p divides the arithmetic derivative of n, and 0 otherwise.

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

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OFFSET

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

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]));