A342187 Numbers k such that both k and k+1 are not exponentially odd numbers.

44, 48, 49, 63, 75, 80, 98, 99, 116, 147, 171, 175, 207, 244, 260, 275, 288, 315, 324, 332, 360, 363, 368, 387, 404, 475, 476, 495, 507, 524, 528, 531, 539, 548, 549, 575, 603, 604, 624, 636, 656, 675, 692, 724, 725, 747, 764, 774, 800, 819, 832, 844, 845, 846

Offset: 1

Author

Amiram Eldar, Mar 04 2021

Keywords

• nonn

Comments

The numbers of terms not exceeding 10^k for k = 2, 3, ..., are 8, 64, 624, 6281, 62779, 627904, 6279725, 62796307, 627961560, ... Apparently this sequence has an asymptotic density 0.062796...

Examples

			44 is a term since 44 = 2^2 * 11 and 45 = 3^2 * 5 both have an even exponent in their prime factorization.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072587, A268335.

Similar sequences: A068140, A068781, A342188, A342189.

Programs

Mathematica

expOddQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], OddQ]; Select[Range[10^3], !expOddQ[#] && !expOddQ[# + 1] &]