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A377993
Number of integers whose arithmetic derivative (A003415) is equal to A024451(n), the arithmetic derivative of the n-th primorial.
2
1, 2, 3, 4, 6, 3, 2, 330, 3, 3
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.
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.
Sequence in context: A203138 A249900 A260272 * A321479 A128332 A074103
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 20 2024
STATUS
approved