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A235991 Numbers with an odd arithmetic derivative, cf. A003415.

%I A235991 #17 Nov 04 2022 14:42:52
%S A235991 2,3,5,6,7,10,11,13,14,17,18,19,22,23,26,27,29,30,31,34,37,38,41,42,
%T A235991 43,45,46,47,50,53,54,58,59,61,62,63,66,67,70,71,73,74,75,78,79,82,83,
%U A235991 86,89,90,94,97,98,99,101,102,103,105,106,107,109,110,113
%N A235991 Numbers with an odd arithmetic derivative, cf. A003415.
%C A235991 A165560(a(n)) = 1; A003415(a(n)) mod 2 = 1;
%C A235991 A007814(a(n)) <= 1, A006519(a(n)) <= 2.
%H A235991 Reinhard Zumkeller, <a href="/A235991/b235991.txt">Table of n, a(n) for n = 1..10000</a>
%F A235991 n is in this sequence iff either n is congruent to 2 modulo 4 or n and Omega(n) are both odd. - _Charlie Neder_, Feb 25 2019
%t A235991 ader[n_] := ader[n] = Switch[n, 0|1, 0, _, If[PrimeQ[n], 1,
%t A235991      Sum[Module[{p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];
%t A235991 Select[Range[120], OddQ[ader[#]]&] (* _Jean-François Alcover_, Oct 10 2021 *)
%o A235991 (Haskell)
%o A235991 a235991 n = a235991_list !! (n-1)
%o A235991 a235991_list = filter (odd . a003415) [0..]
%o A235991 (Python)
%o A235991 from itertools import count, islice
%o A235991 from sympy import factorint
%o A235991 def A235991_gen(startvalue=0): # generator of terms >= startvalue
%o A235991     return filter(lambda n: n&3==2 or (n&1 and sum(factorint(n).values())&1), count(max(startvalue,0)))
%o A235991 A235991_list = list(islice(A235991_gen(),40)) # _Chai Wah Wu_, Nov 04 2022
%Y A235991 Cf. A003415, A006519, A007814, A165560, A235992 (complement), A000040 (subsequence).
%K A235991 nonn
%O A235991 1,1
%A A235991 _Reinhard Zumkeller_, Mar 11 2014