A356158 - OEIS

%I #10 Aug 04 2022 22:27:14

%S 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 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 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 a(n) = gcd(n, A347879(n)).

%C The fixed points of this sequence is given by the union of {2} and A336702.

%H Antti Karttunen, <a href="/A356158/b356158.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = gcd(n, A347879(n)).

%o (PARI)

%o 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 Abinprefix(n,k) = { my(digs=binary(n)); fromdigits(vector(k,i,digs[i]),2); };

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o 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 A348040sq(x,y) = Abincompreflen(A156552(x), A156552(y));

%o A348041sq(x,y) = A005940(1+Abinprefix(A156552(x),A348040sq(x,y)));

%o A347879(n) = A348041sq(n,sigma(n));

%o A356158(n) = gcd(n, A347879(n));

%Y Cf. A000203, A336702, A347879, A348040, A348041.

%Y Cf. also A356156, A356157, A356308.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 30 2022