%I #8 Mar 06 2021 06:00:34
%S 80,624,2511,5264,6399,7695,7856,10287,13040,14640,15471,15632,18063,
%T 19375,20624,20816,23247,23408,25839,27135,28560,28592,31023,31184,
%U 33615,35072,36015,36368,38799,38960,39375,40816,41391,44144,46250,46575,46736,49167,51920
%N Numbers k such that both k and k+1 are not exponentially squarefree numbers.
%C 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...
%H Amiram Eldar, <a href="/A342188/b342188.txt">Table of n, a(n) for n = 1..10000</a>
%e 80 is a term since 80 = 2^4 * 5 and 81 = 3^4 both have a nonsquarefree exponent in their prime factorization.
%t expSqFQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], SquareFreeQ]; Select[Range[5*10^4], !expSqFQ[#] && !expSqFQ[# + 1] &]
%Y Cf. A130897, A209061.
%Y Similar sequences: A068140, A068781, A342187, A342189.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 04 2021