cp's OEIS Frontend

A373382 a(n) = gcd(A329697(n), A331410(n)), where A329697, A331410 give the number of iterations needed to reach a power of 2, when using the map n -> n-(n/p), or respectively, n -> n+(n/p), where p is the largest prime factor of n.

%I A373382 #9 Jun 06 2024 08:23:38
%S A373382 0,0,1,0,1,1,1,0,2,1,2,1,2,1,1,0,1,2,3,1,1,2,1,1,2,2,3,1,1,1,1,0,3,1,
%T A373382 3,2,1,3,3,1,1,1,1,2,1,1,2,1,2,2,2,2,1,3,1,1,4,1,4,1,1,1,1,0,1,3,4,1,
%U A373382 1,3,1,2,1,1,1,3,1,3,1,1,4,1,3,1,1,1,1,2,1,1,1,1,2,2,1,1,1,2,4,2,1,2,3,2,4
%N A373382 a(n) = gcd(A329697(n), A331410(n)), where A329697, A331410 give the number of iterations needed to reach a power of 2, when using the map n -> n-(n/p), or respectively, n -> n+(n/p), where p is the largest prime factor of n.
%C A373382 As A329697 and A331410 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 A373382 Antti Karttunen, <a href="/A373382/b373382.txt">Table of n, a(n) for n = 1..100000</a>
%F A373382 a(n) = gcd(A329697(n), A334861(n)) = gcd(A331410(n), A334861(n)).
%F A373382 a(n) = gcd(A329697(n), A335877(n)) = gcd(A331410(n), A335877(n)).
%o A373382 (PARI)
%o A373382 A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
%o A373382 A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
%o A373382 A373382(n) = gcd(A329697(n), A331410(n));
%Y A373382 Cf. A329697, A331410, A334861, A335877.
%Y A373382 Cf. also A373370.
%K A373382 nonn
%O A373382 1,9
%A A373382 _Antti Karttunen_, Jun 06 2024