A351854 Numbers k such that k and k+1 are both divisible by the number of their divisors over the Eisenstein integers.

1, 2, 80, 3968, 50624, 497024, 505520, 3207680, 6890624, 9150624, 12383360, 12852224, 13549760, 19210688, 20657024, 25250624, 41796224, 41873840, 47900240, 48650624, 79121024, 81450624, 86099840, 132503120, 140920640, 149450624, 174636224, 186732224, 214769024

Offset

1,2

Comments

Numbers k such that A319442(k) | k and A319442(k+1) | k+1.

Except for 1 and 2, all the terms are even numbers of the form k^2 - 1 (A033996).

Links

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

Example

2 is a term since 2 is divisible by A319442(2) = 2 and 3 is divisible by A319442(3) = 3.
80 is a term since 80 is divisible by A319442(80) = 10 and 81 is divisible by A319442(81) = 9.

Mathematica

f[p_, e_] := Switch[Mod[p, 3], 0, 2*e + 1, 1, (e + 1)^2, 2, e + 1]; eisNumDiv[1] = 1; eisNumDiv[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := Divisible[n, eisNumDiv[n]]; Join[{1, 2}, Select[Range[3, 15000, 2]^2 - 1, q[#] && q[# + 1] &]]

Crossrefs

Subsequence of A351853.

Cf. A033996, A114617, A319442, A351852.

Sequence in context: A222826 A123828 A260659 * A210277 A008563 A059487

Adjacent sequences: A351851 A351852 A351853 * A351855 A351856 A351857

Keyword

nonn

Author

Amiram Eldar, Feb 22 2022

Status

approved