cp's OEIS Frontend

A373370 a(n) = gcd(bigomega(n), A064097(n)), where bigomega is number 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 A373370 #7 Jun 05 2024 19:23:05
%S A373370 0,1,1,2,1,1,1,3,2,2,1,1,1,1,1,4,1,1,1,1,2,2,1,1,2,2,3,3,1,3,1,5,1,2,
%T A373370 1,2,1,1,1,2,1,1,1,1,1,2,1,1,2,1,1,1,1,1,2,1,2,2,1,1,1,2,1,6,2,1,1,1,
%U A373370 1,1,1,1,1,2,1,1,1,1,1,1,4,2,1,4,2,1,1,4,1,4,1,3,1,2,1,1,1,3,3,4,1,1,1,4,3
%N A373370 a(n) = gcd(bigomega(n), A064097(n)), where bigomega is number 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 A373370 As A001222 and A064097 are both fully additive sequences, all sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication, i.e., are multiplicative semigroups.
%H A373370 Antti Karttunen, <a href="/A373370/b373370.txt">Table of n, a(n) for n = 1..100000</a>
%o A373370 (PARI)
%o A373370 A064097(n) = if(1==n,0,1+A064097(n-(n/vecmin(factor(n)[,1]))));
%o A373370 A373370(n) = gcd(bigomega(n), A064097(n));
%Y A373370 Cf. A001222, A064097.
%Y A373370 Cf. also A373365, A373366.
%K A373370 nonn
%O A373370 1,4
%A A373370 _Antti Karttunen_, Jun 05 2024