A047779 Abundant or perfect numbers k such that neither k-1 nor k+1 is a prime.

56, 120, 144, 160, 176, 186, 204, 208, 216, 220, 246, 260, 288, 300, 304, 320, 324, 340, 342, 364, 392, 414, 416, 426, 474, 476, 496, 516, 528, 532, 534, 544, 550, 552, 560, 580, 582, 624, 636, 650, 666, 680, 696, 704, 714, 736, 748, 780, 784, 792, 800

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Haskell Program for Abundant and Perfect Numbers [Cached copy at the Wayback Machine].

Example

a(1) = 56 because 55 and 57 are composite and the sum of the divisors of 56 is 64 which is >= 56 and no integer < 56 has this property.

Mathematica

Select[Range[800], DivisorSigma[1, #] >= 2 # && And @@ CompositeQ[# + {-1, 1}] &] (* Amiram Eldar, Feb 09 2020 *)

Prog

(PARI) isok(n) = (sigma(n) >= 2*n) && ! isprime(n-1) && ! isprime(n+1) \\ Michel Marcus, Jun 12 2013

Crossrefs

A023196 is a superset.

Sequence in context: A219458 A054891 A118161 * A044243 A044624 A157330

Adjacent sequences: A047776 A047777 A047778 * A047780 A047781 A047782

Keyword

easy,nonn

Author

Tony Davie (ad(AT)dcs.st-and.ac.uk)

Extensions

More terms from Michel Marcus, Jun 12 2013

Status

approved