A189828 Numbers k for which d(k-1) + d(k+1) is a record, where d(k) is the number of divisors of k.

2, 3, 5, 7, 11, 17, 19, 29, 41, 71, 161, 169, 181, 239, 419, 701, 721, 881, 1079, 1681, 2159, 2519, 2521, 4031, 4159, 5039, 7561, 8399, 10081, 13441, 13859, 18721, 20161, 22679, 25199, 27719, 27721, 35281, 45361, 50399, 50401, 55439, 65519, 110879, 138599

Offset: 1

Author

T. D. Noe, Apr 28 2011

Keywords

• nonn

Comments

Many of these terms are in A090481, which restricts k to be prime. The record values are in A189829.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..135

Crossrefs

Cf. A090481, A189827, A189829.

Programs

Mathematica

DeleteDuplicates[Table[{n,DivisorSigma[0,n-1]+DivisorSigma[0,n+1]},{n,2,140000}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Jul 14 2025 *)