A373369 - OEIS

%I #10 Jun 05 2024 14:49:53

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

%T 2,2,1,1,2,1,1,3,1,3,1,1,1,1,2,3,2,1,1,1,2,1,2,1,1,4,1,1,1,6,2,1,1,3,

%U 2,1,1,1,1,1,1,1,2,3,1,1,4,1,1,2,2,1,2,1,1,1,2,3,2,1,2,1,1,1,1,2,1,1,1,1,3

%N a(n) = gcd(A001414(n), A059975(n)), where A001414 and A059975 are fully additive with a(p) = p and a(p) = p-1, respectively.

%H Antti Karttunen, <a href="/A373369/b373369.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);

%o A059975(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };

%o A373369(n) = gcd(A001414(n), A059975(n));

%Y Cf. A001414, A059975, A345452 (positions of even terms).

%Y Cf. also A082299, A306709, A373362, A373363, A373364, A373365.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jun 05 2024