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a(n) = gcd(n, A243071(n)).
5

%I #12 Jul 17 2023 18:00:00

%S 1,1,3,2,1,6,1,4,1,2,1,12,1,2,1,8,1,2,1,4,1,2,1,24,1,2,9,4,1,2,1,16,1,

%T 2,1,4,1,2,1,8,1,2,43,4,5,2,1,48,1,2,1,4,1,18,1,8,1,2,1,4,1,2,3,32,1,

%U 2,1,4,1,2,1,8,1,2,3,4,11,2,1,16,1,2,1,4,1,86,1,8,1,10,7,4,1,2,1,96,1,2,11,4

%N a(n) = gcd(n, A243071(n)).

%C Primes p such that a(p) = p are those that occur as factors of (2^A000720(p))-1: 3, 43, 49477. Are there any more of them?

%H Antti Karttunen, <a href="/A364256/b364256.txt">Table of n, a(n) for n = 1..16384</a>

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

%o (PARI)

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A243071(n) = if(n<=2, n-1, if(!(n%2), 2*A243071(n/2), 1+(2*A243071(A064989(n)))));

%o A364256(n) = gcd(n, A243071(n));

%Y Cf. A243071.

%Y Cf. also A364254, A364255.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 17 2023