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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A341079 A045456 A115167 * A241043 A045457 A165557

Adjacent sequences: A115100 A115101 A115102 * A115104 A115105 A115106

Keyword

easy,nonn

Author

Cino Hilliard, Mar 02 2006

Status

approved