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A370130
a(n) = A369669(A276086(n)), where A369669 is the greatest common divisor of the first and second arithmetic derivative of n, and A276086 is the primorial base exp-function.
4
0, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 3, 1, 1, 16, 1, 5, 5, 5, 5, 5, 5, 100, 25, 25, 175, 25, 25, 1, 3, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 17, 1, 1, 5, 5, 5, 5, 20, 5, 25, 25, 25, 25, 325, 25, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 11, 1, 4, 1, 1, 1, 1, 1, 5, 5, 320, 95, 5, 5, 25, 25, 25, 25, 100, 25, 7, 7, 112, 7, 7, 7, 7, 7, 7, 7, 28
OFFSET
0,9
FORMULA
a(n) = A369669(A276086(n)).
a(n) = gcd(A327860(n), A370131(n)).
For n >= 1, a(n) = A085731(A327860(n)).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369669(n) = { my(d=A003415(n)); gcd(d, A003415(d)); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
CROSSREFS
Cf. A003415, A068346, A085731, A276086, A327860, A328242 (positions of 1's), A370131.
Sequence in context: A046592 A369875 A334432 * A010326 A196879 A193349
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Feb 10 2024
STATUS
approved