A378057 Composite numbers k such that A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}) = 2.

6, 481, 793, 949, 1417, 2041, 2257, 2509, 2701, 2977, 3133, 3589, 3601, 4033, 4069, 4453, 4849, 5161, 5317, 5809, 5917, 5941, 6697, 7033, 7081, 7141, 7501, 7957, 7969, 8593, 8917, 9217, 9529, 9577, 10249, 10573, 10777, 11041, 11401, 11461, 11581, 11773, 12469, 12913, 12961

Offset: 1

Author

Amiram Eldar, Nov 15 2024

Keywords

• nonn

Comments

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

6 is the only even term.

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A378056.

Programs

Mathematica

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

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);