A378056 a(n) = gcd(A057643(n), A084190(n)) = gcd(lcm{d+1 : d|n}, lcm{d-1 : d > 1 and d|n}).

1, 1, 2, 3, 2, 2, 2, 3, 4, 6, 2, 30, 2, 6, 4, 15, 2, 20, 2, 6, 4, 6, 2, 210, 6, 6, 4, 6, 2, 84, 2, 15, 4, 6, 12, 420, 2, 6, 4, 126, 2, 60, 2, 30, 8, 6, 2, 210, 8, 6, 4, 30, 2, 20, 12, 90, 4, 6, 2, 4620, 2, 6, 40, 45, 6, 84, 2, 6, 4, 36, 2, 420, 2, 6, 24, 30, 12

Offset

1,3

Links

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

Formula

a(n) == 1 (mod 2) if and only if n is a power of 2 (A000079).

a(p) = 2 for an odd prime p. Composite numbers k such that a(k) = 2 are listed in A378057.

Mathematica

a[n_] := Module[{d = Divisors[n]}, GCD[LCM @@ (d + 1), LCM @@ (Rest @ d - 1)]]; a[1] = 1; Array[a, 100]

Prog

(PARI) a(n) = {my(d = divisors(n)); gcd(lcm(apply(x->x+1, d)), lcm(apply(x -> if(x > 1, x-1, x), d))); }

Crossrefs

Cf. A000079, A057643, A084190, A378053, A378057.

Sequence in context: A299229 A289496 A371256 * A248973 A305048 A205717

Adjacent sequences: A378053 A378054 A378055 * A378057 A378058 A378059

Keyword

nonn

Author

Amiram Eldar, Nov 15 2024

Status

approved