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

Author

Jianing Song, Aug 17 2022

Keywords

• nonn
• hard

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.

a(17) = 2^521 - 1 is too large to include here. - Jinyuan Wang, Jan 21 2025

Examples

			See A354532.
		

Crossrefs

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

Programs

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

Formula

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