A354536 - OEIS

%I #14 Aug 17 2022 10:15:41

%S 1,3,7,31,127,511,8191,131071,524287,2147483647,2305843009213693951,

%T 147573952589676412927,618970019642690137449562111,

%U 162259276829213363391578010288127,170141183460469231731687303715884105727,174224571863520493293247799005065324265471

%N Numbers k such that 2*k is in A354525.

%C Numbers k such that for every prime factor p of k we have gpf(2*k+p) = p, gpf = A006530.

%C Numbers k such that for every prime factor p of k, 2*k+p is p-smooth.

%F a(n) = 2^A354531(n) - 1 = A354533(n)/2.

%e See A354532.

%o (PARI) lista(nn,{lim=256},{lim_p=1<<32}) = for(n=1, nn, if(isA354531(n,lim,lim_p), print1(2^n-1, ", "))) \\ See A354531 for the function isA354531

%Y Cf. A006530, A354525, A354531, A354532, A354533, A354537.

%K nonn,hard,more

%O 1,2

%A _Jianing Song_, Aug 17 2022