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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 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.)