A378058 - OEIS

%I #11 Nov 15 2024 12:56:18

%S 1,60,210,360,420,504,630,660,840,924,1092,1260,1320,1560,1848,1980,

%T 2184,2310,2520,2640,2772,3080,3120,3276,3465,3960,4080,4284,4620,

%U 4680,5320,5460,5544,6006,6552,6732,6840,6864,6930,7140,7800,7854,7920,8190,8280,8568,8580,9240,9360,9828

%N Numbers k that divide A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}).

%C After the first term a(1) = 1, the next odd term is a(25) = 3465, the next term that is coprime to 6 is a(308) = 95095, and the next term that is coprime to 30 is a(13544) = 10023013.

%H Amiram Eldar, <a href="/A378058/b378058.txt">Table of n, a(n) for n = 1..10000</a>

%e 60 is a term since A378056(60) = 4620 = 60 * 77 is divisible by 60.

%t s[n_] := Module[{d = Divisors[n]}, GCD[LCM @@ (d + 1), LCM @@ (Rest @ d - 1)]]; s[1] = 1; Select[Range[10000], Divisible[s[#], #] &]

%o (PARI) is(k) = {my(d = divisors(k)); !(lcm(apply(x->x+1, d)) % k) && !(lcm(apply(x -> if(x > 1, x-1, x), d)) % k);}

%Y Intersection of A377950 and A377952.

%Y A378059 is a subsequence.

%Y Cf. A378056, A378054.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 15 2024