A334418 Primitive abundant numbers (A091191) with a record gap to the next primitive abundant number.

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).

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