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A334418
Primitive abundant numbers (A091191) with a record gap to the next primitive abundant number.
3
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
OFFSET
1,1
COMMENTS
The record gap values are 6, 10, 12, 14, 24, 36, 70, 84, ... (see the link for more values).
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
Similar sequences: A306747, A306748, A306953.
Sequence in context: A124672 A289980 A109547 * A269453 A082800 A026041
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 29 2020
STATUS
approved