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

1,1

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...

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A130897, A209061.

Similar sequences: A068140, A068781, A342187, A342189.

Sequence in context: A365887 A107624 A068782 * A255478 A204342 A235090

Adjacent sequences: A342185 A342186 A342187 * A342189 A342190 A342191

Keyword

nonn

Author

Amiram Eldar, Mar 04 2021

Status

approved