A181561 Primes of the form highly abundant number + 1.

2, 3, 5, 7, 11, 13, 17, 19, 31, 37, 43, 61, 73, 97, 109, 181, 211, 241, 337, 421, 541, 601, 631, 661, 1009, 1201, 1621, 1801, 2161, 2341, 2521, 3121, 3361, 4201, 4621, 5881, 6121, 6301, 7561, 8821, 9241, 12241, 12601, 13441, 15121, 16381, 18481, 19801, 20161, 21841, 23761, 30241, 35281

Offset: 1

Author

Jonathan Vos Post, Jan 29 2011

Keywords

• nonn
• easy

Examples

			The 52nd highly abundant number is 1800, add one to get 1801 which is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A000040, A000203, A002093.

Programs

Mathematica

seq = {}; smax = 0; Do[s = DivisorSigma[1, n]; If[s > smax, smax = s; If[PrimeQ[n + 1], AppendTo[seq, n + 1]]], {n, 1, 10^4}]; seq (* Amiram Eldar, Jun 07 2019 *)

Formula

{A002093(i) + 1} INTERSECTION A000040.

{1 + (sigma(n) > sigma(m) for all m < n + 1)} INTERSECTION A000040.