A342188 Numbers k such that both k and k+1 are not exponentially squarefree numbers.

80, 624, 2511, 5264, 6399, 7695, 7856, 10287, 13040, 14640, 15471, 15632, 18063, 19375, 20624, 20816, 23247, 23408, 25839, 27135, 28560, 28592, 31023, 31184, 33615, 35072, 36015, 36368, 38799, 38960, 39375, 40816, 41391, 44144, 46250, 46575, 46736, 49167, 51920

Offset: 1

Author

Amiram Eldar, Mar 04 2021

Keywords

• nonn

Comments

The numbers of terms not exceeding 10^k for k = 2, 3, ..., are 1, 2, 7, 72, 719, 7226, 72238, 722565, 7225651, ... Apparently this sequence has an asymptotic density 0.00007225...

Examples

			80 is a term since 80 = 2^4 * 5 and 81 = 3^4 both have a nonsquarefree exponent in their prime factorization.
		

Links

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

Crossrefs

Cf. A130897, A209061.

Similar sequences: A068140, A068781, A342187, A342189.

Programs

Mathematica

expSqFQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], SquareFreeQ]; Select[Range[5*10^4], !expSqFQ[#] && !expSqFQ[# + 1] &]