A115103 Primes p such that p-1 and p+1 have the same number of prime factors with multiplicity.

5, 19, 29, 43, 67, 89, 151, 173, 197, 233, 271, 283, 307, 317, 349, 461, 491, 569, 571, 593, 653, 701, 739, 751, 787, 857, 859, 907, 919, 1013, 1061, 1097, 1277, 1291, 1303, 1483, 1667, 1747, 1831, 1867, 1889, 1913, 1973, 2003, 2083, 2131, 2311, 2357, 2393

Offset: 1

Author

Cino Hilliard, Mar 02 2006

Keywords

• easy
• nonn

Examples

			19-1 = 2*3*3 has 3 factors. 19+1 = 2*2*5 has 3 factors. So 19 is in the table.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Crossrefs

Cf. A067386 (without multiplicity), A323498, A323536, A323537.

Programs

Maple

isA115103 := proc(n)
    if not type(n,prime) then
        return false;
    end if;
    if numtheory[bigomega](n-1) <> numtheory[bigomega](n+1) then
        false;
    else
        true ;
    end if ;
end proc:
for n from 2 to 3000 do
    if isA115103(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Feb 13 2019
# second Maple program:
q:= p-> isprime(p) and (f-> f(p+1)=f(p-1))(numtheory[bigomega]):
select(q, [$1..3000])[];  # Alois P. Heinz, May 08 2022

Mathematica

Select[Prime[Range[400]],PrimeOmega[#-1]==PrimeOmega[#+1]&] (* Harvey P. Dale, Apr 26 2014 *)

PARI

g(n) = forprime(x=1,n,p1=bigomega(x-1);p2=bigomega(x+1);if(p1==p2,print1(x",")))