A354536 Numbers k such that 2*k is in A354525.

1, 3, 7, 31, 127, 511, 8191, 131071, 524287, 2147483647, 2305843009213693951, 147573952589676412927, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727, 174224571863520493293247799005065324265471

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..16.

Formula

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

Example

See A354532.

Prog

(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

Crossrefs

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

Sequence in context: A138865 A051281 A145038 * A138864 A105768 A084924

Adjacent sequences: A354533 A354534 A354535 * A354537 A354538 A354539

Keyword

nonn,hard,more

Author

Jianing Song, Aug 17 2022

Status

approved