%I #7 Nov 15 2024 12:56:40

%S 6,481,793,949,1417,2041,2257,2509,2701,2977,3133,3589,3601,4033,4069,

%T 4453,4849,5161,5317,5809,5917,5941,6697,7033,7081,7141,7501,7957,

%U 7969,8593,8917,9217,9529,9577,10249,10573,10777,11041,11401,11461,11581,11773,12469,12913,12961

%N Composite numbers k such that A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}) = 2.

%C A378056(p) = 2 for all odd primes p.

%C 6 is the only even term.

%C The least term that is not a semiprime is a(114) = 29341 = 13 * 37 * 61, and the least term that has more than 3 distinct prime factors is a(4087545) = 1038565321 = 37 * 61 * 421 * 1093.

%H Amiram Eldar, <a href="/A378057/b378057.txt">Table of n, a(n) for n = 1..10000</a>

%t s[n_] := Module[{d = Divisors[n]}, GCD[LCM @@ (d + 1), LCM @@ (Rest @ d - 1)]]; s[1] = 1; Select[Range[13000], CompositeQ[#] && s[#] == 2 &]

%o (PARI) is(k) = if(isprime(k), 0, my(d = divisors(k)); gcd(lcm(apply(x->x+1, d)), lcm(apply(x -> if(x > 1, x-1, x), d))) == 2);

%Y Cf. A378056.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 15 2024