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 A351854 Numbers k such that k and k+1 are both divisible by the number of their divisors over the Eisenstein integers. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 7 09:14 EDT 2024. Contains 375730 sequences. (Running on oeis4.)