

A342188


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


3



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
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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: A233351 A107624 A068782 * A255478 A204342 A235090
Adjacent sequences: A342185 A342186 A342187 * A342189 A342190 A342191


KEYWORD

nonn


AUTHOR

Amiram Eldar, Mar 04 2021


STATUS

approved



