A377993 Number of integers whose arithmetic derivative (A003415) is equal to A024451(n), the arithmetic derivative of the n-th primorial.

1, 2, 3, 4, 6, 3, 2, 330, 3, 3

Offset: 2

Author

Antti Karttunen, Nov 20 2024

Keywords

• nonn

Comments

a(n) is the number of natural numbers k such that k' = A003415(k) = A024451(n). The solutions k are listed in A377992.

For 1! = 1, there is an infinite number of integers k for which k' = 1 (all the primes), therefore the starting offset is 2.

Examples

			There is just one number such that A003415(k) = A024451(2) = 5, and that is k=6, therefore a(2) = 1.
There are two numbers such that A003415(k) = A024451(3) = 31, and they are k=30 and k=58, therefore a(3) = 2.
		

Links

• Index entries for sequences related to primorial numbers

Crossrefs

Row lengths of A377992.

Cf. A002620, A003415, A024451, A099302.

Formula

a(n) = A099302(A024451(n)).

a(n) = Sum_{k=1..A002620(A024451(n))} [A003415(k) = A024451(n)], where [ ] is the Iverson bracket.