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 A334418 Primitive abundant numbers (A091191) with a record gap to the next primitive abundant number. 2
 12, 20, 30, 42, 114, 138, 678, 1758, 8296, 10052, 12966, 13076, 14862, 19635, 38950, 50802, 77118, 94108, 218334, 439134, 478194, 746202, 1128174, 2028198, 6934398, 7750146, 8330924, 10030804, 33467106, 36205482, 60716562, 65183838, 69334698, 81757564, 84010614 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The record gap values are 6, 10, 12, 14, 24, 36, 70, 84, ... (see the link for more values). LINKS Amiram Eldar, Table of n, a(n) for n = 1..42 Amiram Eldar, Table of n, a(n), gap(n) for n = 1..42 EXAMPLE 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. MATHEMATICA 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 CROSSREFS Cf. A091191, A283418, A334419. Similar sequences: A306747, A306748, A306953. Sequence in context: A124672 A289980 A109547 * A269453 A082800 A026041 Adjacent sequences:  A334415 A334416 A334417 * A334419 A334420 A334421 KEYWORD nonn AUTHOR Amiram Eldar, Apr 29 2020 STATUS approved

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Last modified May 15 15:29 EDT 2021. Contains 343920 sequences. (Running on oeis4.)