A334419 Primitive abundant numbers (A071395) with a record gap to the next primitive abundant number.

20, 104, 945, 2210, 2584, 8415, 10184, 12104, 15368, 86272, 133484, 135470, 140668, 643336, 700256, 1149952, 2410816, 2434888, 5924032, 6100605, 7623872, 8531144, 8760424, 9405045, 10471755, 14803216, 16283085, 21506432, 26919250, 34441946, 35622016, 36064964

Offset: 1

Author

Amiram Eldar, Apr 29 2020

Keywords

• nonn

Comments

The record gap values are 50, 168, 239, 260, 406, 510, ... (see the link for more values).

Examples

			The first 5 terms of A071395 are 20, 70, 88, 104 and 272. The differences between these terms are 50, 18, 16, and 168. The record gaps are 50 and 168, which occur after the terms 20 and 104.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..59
• Amiram Eldar, Table of n, a(n), gap(n) for n = 1..59

Crossrefs

Cf. A071395, A330872, A334418.

Similar sequences: A306747, A306748, A306953.

Programs

Mathematica

primAbQ[n_] := DivisorSigma[1, n] > 2 n && AllTrue[Most @ Rest @ Divisors[n], DivisorSigma[1, #] < 2*# &]; seq = {}; m = 20; dm = 0; Do[If[primAbQ[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 21, 10^6}]; seq