A133855 Primes p such that p-1 and p+1 are abundant numbers.

19, 41, 71, 79, 89, 101, 103, 113, 139, 197, 199, 223, 271, 281, 307, 349, 353, 367, 379, 401, 439, 449, 461, 463, 491, 499, 521, 571, 607, 617, 619, 641, 643, 701, 727, 739, 761, 769, 811, 821, 859, 881, 911, 919, 929, 941, 953, 967, 991, 1039, 1061, 1063

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 Harvey P. Dale)

Example

19-1 = 18 = 2*3*3, sigma(18)/18 = 39/18 > 2, 18 is abundant, 19+1 = 20 = 2*2*5, sigma(20)/20  = 42/20 > 2, 20 is abundant, so a(1) = 19.

Maple

with(numtheory): a:=proc(n) if isprime(n)=true and 0<sigma(n-1)-2*n+2 and 0< sigma(n+1)-2*n-2 then n else end if end proc: seq(a(n), n=2..1000); # Emeric Deutsch, Jan 26 2008

Mathematica

Select[Prime[Range[500]], (Plus @@ Divisors[ # - 1]) > 2*(# - 1) && (Plus @@ Divisors[ # + 1]) > 2*(# + 1) &] (* Stefan Steinerberger, Jan 21 2008 *)
Select[Prime[Range[180]], Min[DivisorSigma[-1, # + {-1, 1}]] > 2 &] (* Amiram Eldar, Jul 01 2022 *)

Prog

(PARI) is(n)=sigma(if(n%6==1, n+1, n-1), -1)>2 && isprime(n) \\ Charles R Greathouse IV, Aug 29 2015

Crossrefs

Cf. A000203, A005101.

Sequence in context: A155024 A323391 A248339 * A280170 A262608 A141855

Adjacent sequences: A133852 A133853 A133854 * A133856 A133857 A133858

Keyword

nonn

Author

Pierre CAMI, Jan 07 2008

Extensions

Corrected and extended by Stefan Steinerberger and Emeric Deutsch, Jan 21 2008

Status

approved