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A373145
a(n) = gcd(A003415(n), A276085(n)), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.
17
0, 1, 1, 2, 1, 1, 1, 3, 2, 7, 1, 4, 1, 1, 8, 4, 1, 1, 1, 8, 2, 1, 1, 1, 2, 1, 3, 32, 1, 1, 1, 5, 2, 1, 12, 6, 1, 1, 8, 1, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 4, 8, 1, 1, 8, 1, 2, 1, 1, 2, 1, 1, 17, 6, 6, 1, 1, 8, 2, 1, 1, 1, 1, 1, 1, 16, 6, 1, 1, 2, 4, 1, 1, 2, 2, 1, 8, 1, 1, 1, 20, 4, 2, 1, 12, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1
OFFSET
1,4
LINKS
FORMULA
a(n) = gcd(A003415(n), A373146(n)) = gcd(A276085(n), A373146(n)).
For n > 1, a(n) = gcd(A276085(n), A373147(n)) = gcd(A003415(n), A373148(n)).
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A002110(n) = prod(i=1, n, prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A373145(n) = gcd(A003415(n), A276085(n));
CROSSREFS
Cf. A368998 (positions of even terms), A368999 (of odd terms), A373144 (of multiples of 3).
Cf. also A327858.
Sequence in context: A254055 A373367 A373362 * A096815 A193516 A124445
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 26 2024
STATUS
approved