cp's OEIS Frontend

A356158 a(n) = gcd(n, A347879(n)).

%I A356158 #10 Aug 04 2022 22:27:14
%S A356158 1,2,1,2,1,6,1,2,1,2,1,3,1,1,3,2,1,2,1,10,1,2,1,6,1,1,1,28,1,2,1,2,3,
%T A356158 2,1,2,1,1,1,1,1,3,1,1,3,2,1,3,1,2,1,2,1,2,1,1,1,1,1,3,1,1,1,2,5,2,1,
%U A356158 1,3,2,1,2,1,1,1,1,1,1,1,5,1,1,1,1,1,1,3,1,1,3,1,1,1,2,1,3,1,2,1,2,1,2,1,1,3
%N A356158 a(n) = gcd(n, A347879(n)).
%C A356158 The fixed points of this sequence is given by the union of {2} and A336702.
%H A356158 Antti Karttunen, <a href="/A356158/b356158.txt">Table of n, a(n) for n = 1..65537</a>
%H A356158 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A356158 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A356158 a(n) = gcd(n, A347879(n)).
%o A356158 (PARI)
%o A356158 Abincompreflen(n, m) = { my(x=binary(n),y=binary(m),u=min(#x,#y)); for(i=1,u,if(x[i]!=y[i],return(i-1))); (u);};
%o A356158 Abinprefix(n,k) = { my(digs=binary(n)); fromdigits(vector(k,i,digs[i]),2); };
%o A356158 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A356158 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A356158 A348040sq(x,y) = Abincompreflen(A156552(x), A156552(y));
%o A356158 A348041sq(x,y) = A005940(1+Abinprefix(A156552(x),A348040sq(x,y)));
%o A356158 A347879(n) = A348041sq(n,sigma(n));
%o A356158 A356158(n) = gcd(n, A347879(n));
%Y A356158 Cf. A000203, A336702, A347879, A348040, A348041.
%Y A356158 Cf. also A356156, A356157, A356308.
%K A356158 nonn
%O A356158 1,2
%A A356158 _Antti Karttunen_, Jul 30 2022