A374116 a(n) = gcd(A328768(n), A328845(n)), where A328768 is the first primorial based variant and A328845 is the first Fibonacci-based variant of the arithmetic derivative, respectively.

0, 0, 1, 2, 4, 1, 7, 1, 12, 12, 1, 1, 20, 1, 1, 1, 32, 1, 33, 1, 4, 1, 1, 1, 52, 10, 1, 54, 4, 1, 1, 1, 80, 1, 1, 4, 84, 1, 1, 1, 4, 1, 1, 1, 4, 3, 1, 1, 128, 14, 5, 1, 4, 1, 135, 4, 4, 1, 1, 1, 4, 1, 1, 3, 192, 6, 1, 1, 4, 1, 1, 1, 204, 1, 1, 10, 4, 2, 1, 1, 16, 216, 1, 1, 4, 6, 1, 1, 4, 1, 3, 360, 4, 1, 1, 24, 304, 1, 7, 3, 20

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i, 1])-1)/f[i, 1]));
A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])/f[i, 1]));
A374116(n) = gcd(A328768(n), A328845(n));

Crossrefs

Cf. A328768, A328845.

Cf. also A374035, A374106.

Sequence in context: A143350 A302541 A119303 * A256107 A207610 A207616

Adjacent sequences: A374113 A374114 A374115 * A374119 A374120 A374121

Keyword

nonn,new

Author

Antti Karttunen, Jun 28 2024

Status

approved