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

Author

Amiram Eldar, Apr 29 2020

Keywords

• nonn

Comments

The record gap values are 6, 10, 12, 14, 24, 36, 70, 84, ... (see the link for more values).

Examples

			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.
		

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

Crossrefs

Cf. A091191, A283418, A334419.

Similar sequences: A306747, A306748, A306953.

Programs

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