A378054 -id:A378054 - cp's OEIS frontend

A378058 Numbers k that divide A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}).

1, 60, 210, 360, 420, 504, 630, 660, 840, 924, 1092, 1260, 1320, 1560, 1848, 1980, 2184, 2310, 2520, 2640, 2772, 3080, 3120, 3276, 3465, 3960, 4080, 4284, 4620, 4680, 5320, 5460, 5544, 6006, 6552, 6732, 6840, 6864, 6930, 7140, 7800, 7854, 7920, 8190, 8280, 8568, 8580, 9240, 9360, 9828

Offset: 1

Amiram Eldar, Nov 15 2024

nonn

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.

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

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

Intersection of A377950 and A377952.
A378059 is a subsequence.
Cf. A378056, A378054.

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

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

A378055 Numbers k such that k | A378053(k) and (k+1) | A378053(k+1).

Original entry on oeis.org

638000, 13466816, 14753024, 16092999, 19494189, 38137749, 63668079, 80061344, 86119704, 107232255, 112375899, 121550624, 127205000, 154466675, 294147854, 391738599, 553140224, 561712095, 682199595, 728999999, 871651143, 879207615, 911062844, 920985624, 1017609999

Offset: 1

Amiram Eldar, Nov 15 2024

nonn

Intersection of A355332 and A377949.
Subsequence of A378054.
Cf. A020696, A377484, A378053, A378059.

q[n_] := q[n] = And @@ Divisible[{Times @@ ((d = Divisors[n]) + 1), Times @@ (Rest@d - 1)}, n]; Select[Range[2*10^7], q[#] && q[# + 1] &]

is1(k) = if(k == 1, 1, my(d = divisors(k)); !(gcd(prod(k=1, #d, d[k]+1), prod(k=2, #d, d[k]-1)) % k));
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

cp's OEIS Frontend

A378058 Numbers k that divide A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}).

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