A235991 - OEIS

%I #17 Nov 04 2022 14:42:52

%S 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 43,45,46,47,50,53,54,58,59,61,62,63,66,67,70,71,73,74,75,78,79,82,83,

%U 86,89,90,94,97,98,99,101,102,103,105,106,107,109,110,113

%N Numbers with an odd arithmetic derivative, cf. A003415.

%C A165560(a(n)) = 1; A003415(a(n)) mod 2 = 1;

%C A007814(a(n)) <= 1, A006519(a(n)) <= 2.

%H Reinhard Zumkeller, <a href="/A235991/b235991.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 ader[n_] := ader[n] = Switch[n, 0|1, 0, _, If[PrimeQ[n], 1,

%t      Sum[Module[{p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];

%t Select[Range[120], OddQ[ader[#]]&] (* _Jean-François Alcover_, Oct 10 2021 *)

%o (Haskell)

%o a235991 n = a235991_list !! (n-1)

%o a235991_list = filter (odd . a003415) [0..]

%o (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A235991_gen(startvalue=0): # generator of terms >= startvalue

%o     return filter(lambda n: n&3==2 or (n&1 and sum(factorint(n).values())&1), count(max(startvalue,0)))

%o A235991_list = list(islice(A235991_gen(),40)) # _Chai Wah Wu_, Nov 04 2022

%Y Cf. A003415, A006519, A007814, A165560, A235992 (complement), A000040 (subsequence).

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 11 2014