A377993 - OEIS

%I #9 Nov 22 2024 20:32:18

%S 1,2,3,4,6,3,2,330,3,3

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

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

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

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

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

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

%e There is just one number such that A003415(k) = A024451(2) = 5, and that is k=6, therefore a(2) = 1.

%e There are two numbers such that A003415(k) = A024451(3) = 31, and they are k=30 and k=58, therefore a(3) = 2.

%Y Row lengths of A377992.

%Y Cf. A002620, A003415, A024451, A099302.

%K nonn

%O 2,2

%A _Antti Karttunen_, Nov 20 2024