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A133855 Primes p such that p-1 and p+1 are abundant numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

19-1=18=2*3*3, s/n=39/18>2, 18 is abundant,

19+1=20=2*2*5, s/n=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 *)

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

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

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)