cp's OEIS Frontend

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

%I A351854 #10 Feb 23 2022 02:33:57
%S A351854 1,2,80,3968,50624,497024,505520,3207680,6890624,9150624,12383360,
%T A351854 12852224,13549760,19210688,20657024,25250624,41796224,41873840,
%U A351854 47900240,48650624,79121024,81450624,86099840,132503120,140920640,149450624,174636224,186732224,214769024
%N A351854 Numbers k such that k and k+1 are both divisible by the number of their divisors over the Eisenstein integers.
%C A351854 Numbers k such that A319442(k) | k and A319442(k+1) | k+1.
%C A351854 Except for 1 and 2, all the terms are even numbers of the form k^2 - 1 (A033996).
%H A351854 Amiram Eldar, <a href="/A351854/b351854.txt">Table of n, a(n) for n = 1..10000</a>
%e A351854 2 is a term since 2 is divisible by A319442(2) = 2 and 3 is divisible by A319442(3) = 3.
%e A351854 80 is a term since 80 is divisible by A319442(80) = 10 and 81 is divisible by A319442(81) = 9.
%t A351854 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] &]]
%Y A351854 Subsequence of A351853.
%Y A351854 Cf. A033996, A114617, A319442, A351852.
%K A351854 nonn
%O A351854 1,2
%A A351854 _Amiram Eldar_, Feb 22 2022