A215068 Numbers n such that for all divisors d of n, d+1 is either a prime or a perfect power.

1, 2, 3, 4, 6, 7, 8, 12, 16, 24, 31, 48, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

Offset

1,2

Comments

Apparently the divisors of 48 (A018261) together with the Mersenne primes (A000668).

Confirmed by Robert Israel, Aug 02 2020: see link.

Next term > 2*10^8.

Links

Table of n, a(n) for n=1..21.

Robert Israel, Proof of conjecture in A215068

Maple

sort([op(numtheory:-divisors(48)), seq(numtheory:-mersenne([i]), i=2..12)]); # Robert Israel, Aug 02 2020

Prog

(PARI)
isA215068(n)=
{
    my(x);
    fordiv (n, d,
        d1 = d + 1;
        if ( isprime(d1) || ispower(d1), next() );
        return(0);
    );
    return(1);
}
for (n=1, 10^9, if(isA215068(n), print1(n, ", ")));

Crossrefs

Cf. A018261 (divisors of 48), A000668 (Mersenne primes), A001597 (perfect powers).

Sequence in context: A018314 A212216 A199639 * A239011 A070525 A283112

Adjacent sequences: A215065 A215066 A215067 * A215069 A215070 A215071

Keyword

nonn,hard

Author

Joerg Arndt, Aug 02 2012

Status

approved