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

1,1

Comments

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

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

Example

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.

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

Crossrefs

Cf. A071395, A330872, A334418.

Similar sequences: A306747, A306748, A306953.

Sequence in context: A088831 A063785 A181703 * A187756 A248087 A209547

Adjacent sequences: A334416 A334417 A334418 * A334420 A334421 A334422

Keyword

nonn

Author

Amiram Eldar, Apr 29 2020

Status

approved