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 A358484 Numbers k such that k, k+1 and k+2 are all bi-unitary abundant numbers (A292982). 1

%I #10 Nov 19 2022 04:47:49

%S 268005374,600350750,2666847104,2683146464,2695309694,2849458688,

%T 3904592768,4112553248,5368737374,6554410784,6955574624,8207456894,

%U 8967010688,9220179968,9868366430,10529171288,12147283070,12411630944,12491149670,13911605630,14126720894,14396391008

%N Numbers k such that k, k+1 and k+2 are all bi-unitary abundant numbers (A292982).

%H Amiram Eldar, <a href="/A358484/b358484.txt">Table of n, a(n) for n = 1..1546</a> (terms below 10^12)

%e 268005374 is in the sequence since 268005374, 268005375 and 268005376 are all bi-unitary abundant numbers (A292982): bsigma(268005374) = 568995840 > 2 * 268005374, bsigma(268005375) = 540633600 > 2 * 268005375, and bsigma(268005376) = 541258200 > 2 * 268005376 (bsigma is the sum of bi-unitary divisors, A188999).

%t f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - If[OddQ[e], 0, p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ f @@@ FactorInteger[n]; abQ[n_] := bsigma[n] > 2*n; v = Cases[Import["https://oeis.org/A096536/b096536.txt", "Table"], {_, _}][[;; , 2]]; Select[v, And @@ abQ /@ (# + {0, 1, 2}) &]

%Y Subsequence of A096536, A292982 and A318167.

%Y Cf. A188999.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 18 2022

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)