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Numbers k such that both k and k+1 are not exponentially odd numbers.
3

%I #9 Mar 06 2021 06:00:15

%S 44,48,49,63,75,80,98,99,116,147,171,175,207,244,260,275,288,315,324,

%T 332,360,363,368,387,404,475,476,495,507,524,528,531,539,548,549,575,

%U 603,604,624,636,656,675,692,724,725,747,764,774,800,819,832,844,845,846

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

%C 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...

%H Amiram Eldar, <a href="/A342187/b342187.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%Y Cf. A072587, A268335.

%Y Similar sequences: A068140, A068781, A342188, A342189.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 04 2021