cp's OEIS Frontend

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

%I A215068 #16 Aug 02 2020 21:24:26
%S A215068 1,2,3,4,6,7,8,12,16,24,31,48,127,8191,131071,524287,2147483647,
%T A215068 2305843009213693951,618970019642690137449562111,
%U A215068 162259276829213363391578010288127,170141183460469231731687303715884105727
%N A215068 Numbers n such that for all divisors d of n, d+1 is either a prime or a perfect power.
%C A215068 Apparently the divisors of 48 (A018261) together with the Mersenne primes (A000668).
%C A215068 Confirmed by _Robert Israel_, Aug 02 2020: see link.
%C A215068 Next term > 2*10^8.
%H A215068 Robert Israel, <a href="/A215068/a215068.pdf">Proof of conjecture in A215068</a>
%p A215068 sort([op(numtheory:-divisors(48)), seq(numtheory:-mersenne([i]),i=2..12)]); # _Robert Israel_, Aug 02 2020
%o A215068 (PARI)
%o A215068 isA215068(n)=
%o A215068 {
%o A215068     my(x);
%o A215068     fordiv (n, d,
%o A215068         d1 = d + 1;
%o A215068         if ( isprime(d1) || ispower(d1), next() );
%o A215068         return(0);
%o A215068     );
%o A215068     return(1);
%o A215068 }
%o A215068 for (n=1,10^9, if(isA215068(n), print1(n,", ")));
%Y A215068 Cf. A018261 (divisors of 48), A000668 (Mersenne primes), A001597 (perfect powers).
%K A215068 nonn,hard
%O A215068 1,2
%A A215068 _Joerg Arndt_, Aug 02 2012