A378058 -id:A378058 - cp's OEIS frontend

A378054 Numbers k that divide A378053(k) = gcd(Product_{d|k} (d + 1), Product_{d|k, d>1} (d - 1)).

1, 60, 90, 120, 144, 168, 180, 210, 240, 252, 280, 336, 360, 420, 504, 540, 560, 630, 660, 720, 840, 900, 924, 990, 1008, 1056, 1080, 1092, 1200, 1260, 1320, 1404, 1440, 1512, 1560, 1680, 1800, 1848, 1872, 1890, 1980, 2016, 2100, 2112, 2160, 2184, 2310, 2376, 2400

Offset: 1

Amiram Eldar, Nov 15 2024

nonn

After the first term a(1) = 1, the next odd term is a(71) = 3465, the next term that is coprime to 6 is a(1058) = 95095, and the next term that is coprime to 30 is a(12174) = 2263261.

			60 is a term since A378053(60) = 166320 = 60 * 2772 is divisible by 60.

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

Intersection of A056954 and A355331.
A378055 is a subsequence.
Cf. A020696, A377484, A378053, A378058.

Select[Range[2500], And @@ Divisible[{Times @@ ((d = Divisors[#]) + 1), Times @@ (Rest @ d - 1)}, #] &]

is(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));

A378059 Numbers k such k | A378056(k) and (k+1) | A378056(k+1).

Original entry on oeis.org

112375899, 871651143, 1525038515, 3524721824, 6058144224, 7616307699, 7929320399, 9778346864, 10799650575, 11536526000, 13663711775, 20596306224, 22326106256, 24442111385, 26385908912, 27394105760, 28476579725, 31552570400, 34148839725, 36045427040, 40916036304, 44037977984, 44430326199

Offset: 1

Amiram Eldar, Nov 15 2024

nonn

Intersection of A377951 and A377953.
Subsequence of A378058.
Cf. A378055, A378056.

is1(k) = {my(d = divisors(k)); !(lcm(apply(x->x+1, d)) % k) && !(lcm(apply(x -> if(x > 1, x-1, x), d)) % 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

A378054 Numbers k that divide A378053(k) = gcd(Product_{d|k} (d + 1), Product_{d|k, d>1} (d - 1)).

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