A181562 Primes of the form highly abundant number - 1.

2, 3, 5, 7, 11, 17, 19, 23, 29, 41, 47, 59, 71, 83, 89, 107, 167, 179, 239, 359, 419, 479, 503, 599, 659, 719, 839, 1259, 1439, 1559, 1619, 1979, 2099, 2339, 2399, 2879, 3023, 3119, 3359, 3779, 4679, 5039, 5879, 6299, 6719, 7559, 7919, 8819, 9239, 10079, 12239, 13859, 21839, 22679, 35279

Offset: 1

Author

Jonathan Vos Post, Jan 29 2011

Keywords

• nonn
• easy

Comments

Note that this sequence and A181561 have an intersection beginning {2, 3, 5, 7, 11, 17, 19, ...}. This sequence UNION A181561 might be called nearly highly abundant primes. That union begins: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 71, 73, 83, 89, 97, 107, 109, 167, 179, 181, 211, 239, 241, 337, 359, 419, 421, 479, 503, 541, 599, 601, 631, 659, 661, 719, 839, 1009, 1201, 1439, 1559, 1619, 1621, 1979, 1801, 2099} and thus has twin nearly highly abundant prime pairs: {(3,5), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73), (107,109), (179,181), (239,241), (419,421), (599,601), (659,661), (1619,1621), ...}.

Examples

			The 55th highly abundant number is 2100; subtract one to get 2099, which is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1588

Crossrefs

Cf. A000040, A000203, A002093, A181561.

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.

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