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%I #11 Apr 30 2020 03:25:37
%S 12,20,30,42,114,138,678,1758,8296,10052,12966,13076,14862,19635,
%T 38950,50802,77118,94108,218334,439134,478194,746202,1128174,2028198,
%U 6934398,7750146,8330924,10030804,33467106,36205482,60716562,65183838,69334698,81757564,84010614
%N Primitive abundant numbers (A091191) with a record gap to the next primitive abundant number.
%C The record gap values are 6, 10, 12, 14, 24, 36, 70, 84, ... (see the link for more values).
%H Amiram Eldar, <a href="/A334418/b334418.txt">Table of n, a(n) for n = 1..42</a>
%H Amiram Eldar, <a href="/A334418/a334418.txt">Table of n, a(n), gap(n) for n = 1..42</a>
%e The first 6 terms of A091191 are 12, 18, 20, 30, 42 and 56. The differences between these terms are 6, 2, 10, 12 and 14. The record gaps are 6, 10, 12 and 14, which occur after the terms 12, 20, 30 and 42.
%t primAbQ[n_] := DivisorSigma[1, n] > 2 n && AllTrue[Most @ Rest @ Divisors[n], DivisorSigma[1, #] <= 2*# &]; seq = {}; m = 12; dm = 0; Do[If[primAbQ[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 13, 10^6}]; seq
%Y Cf. A091191, A283418, A334419.
%Y Similar sequences: A306747, A306748, A306953.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 29 2020
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