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, 2, 1, 3, 6

Offset

2,2

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.

Links

Table of n, a(n) for n=2..15.

Index entries for sequences related to primorial numbers

Formula

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

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

Example

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.

Crossrefs

Row lengths of A377992.

Cf. A002620, A003415, A024451, A099302.

Sequence in context: A203138 A249900 A260272 * A321479 A128332 A074103

Adjacent sequences: A377990 A377991 A377992 * A377994 A377995 A377996

Keyword

nonn,more

Author

Antti Karttunen, Nov 20 2024

Extensions

a(12)-a(15) from Max Alekseyev, Nov 07 2025

Status

approved