cp's OEIS Frontend

A373365 a(n) = gcd(A001414(n), A064097(n)), where A001414 is the sum of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.

%I A373365 #8 Jun 03 2024 00:27:10
%S A373365 0,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,1,1,1,1,2,1,1,1,2,3,3,1,1,2,1,5,7,1,
%T A373365 1,2,1,7,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,8,1,2,1,1,1,1,1,1,6,2,8,1,7,
%U A373365 1,2,1,1,1,1,1,1,9,2,1,1,4,1,1,2,2,9,1,1,1,1,1,9,1,1,3,1,1,1,1,2,1,2,1,1,3
%N A373365 a(n) = gcd(A001414(n), A064097(n)), where A001414 is the sum of prime factors with repetition, and A064097 is a quasi-logarithm defined inductively by a(1) = 0 and a(p) = 1 + a(p-1) if p is prime and a(n*m) = a(n) + a(m) if m,n > 1.
%C A373365 As A001414 and A064097 are both fully additive sequences, all sequences that give the positions of multiples of some k > 1 in this sequence are closed under multiplication.
%H A373365 Antti Karttunen, <a href="/A373365/b373365.txt">Table of n, a(n) for n = 1..100000</a>
%o A373365 (PARI)
%o A373365 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A373365 A064097(n) = if(1==n,0,1+A064097(n-(n/vecmin(factor(n)[,1]))));
%o A373365 A373365(n) = gcd(A001414(n), A064097(n));
%Y A373365 Cf. A001414, A064097.
%Y A373365 Cf. also A082299, A373362, A373363, A373364, A373366.
%K A373365 nonn
%O A373365 1,4
%A A373365 _Antti Karttunen_, Jun 02 2024