A374112 - OEIS

%I #6 Jun 29 2024 09:33:25

%S 0,1,2,2,1,3,1,3,4,1,1,4,1,1,1,4,1,5,1,1,1,1,1,5,2,1,6,1,1,1,1,5,1,1,

%T 18,6,1,1,1,1,1,1,1,1,1,1,1,6,2,1,1,1,1,7,2,1,1,1,1,1,1,1,17,6,2,1,1,

%U 1,1,1,1,7,1,1,2,1,6,1,1,1,8,1,1,17,6,1,1,1,1,1,6,1,1,1,2,7,1,1,1,2,1,1,1,1,2

%N a(n) = gcd(A113177(n), A276085(n)), where A113177 and A276085 are fully additive with a(p) = Fibonacci(p) and a(p) = p#/p, respectively.

%H Antti Karttunen, <a href="/A374112/b374112.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])));

%o A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };

%o A374112(n) = gcd(A113177(n), A276085(n));

%Y Cf. A113177, A276085, A374113, A374114 (indices of even terms), A374115 (of odd terms).

%Y Cf. also A374116.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 29 2024