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

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.

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]));
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

Adjacent sequences: A368912 A368913 A368914 * A368916 A368917 A368918

Keyword

nonn

Author

Antti Karttunen, Jan 09 2024

Status

approved