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

Author

Amiram Eldar, Feb 22 2022

Keywords

• nonn

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).

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A351853.

Cf. A033996, A114617, A319442, A351852.

Programs

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] &]]