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A215068 Numbers n such that for all divisors d of n, d+1 is either a prime or a perfect power. 1
1, 2, 3, 4, 6, 7, 8, 12, 16, 24, 31, 48, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Joerg Arndt, Aug 02 2012

STATUS

approved

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Last modified August 10 11:52 EDT 2020. Contains 336379 sequences. (Running on oeis4.)