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 A235991 Numbers with an odd arithmetic derivative, cf. A003415. 27
 2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 18, 19, 22, 23, 26, 27, 29, 30, 31, 34, 37, 38, 41, 42, 43, 45, 46, 47, 50, 53, 54, 58, 59, 61, 62, 63, 66, 67, 70, 71, 73, 74, 75, 78, 79, 82, 83, 86, 89, 90, 94, 97, 98, 99, 101, 102, 103, 105, 106, 107, 109, 110, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A165560(a(n)) = 1; A003415(a(n)) mod 2 = 1; A007814(a(n)) <= 1, A006519(a(n)) <= 2. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA 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 MATHEMATICA ader[n_] := ader[n] = Switch[n, 0|1, 0, _, If[PrimeQ[n], 1, Sum[Module[{p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]]; Select[Range[120], OddQ[ader[#]]&] (* Jean-François Alcover, Oct 10 2021 *) PROG (Haskell) a235991 n = a235991_list !! (n-1) a235991_list = filter (odd . a003415) [0..] (Python) from itertools import count, islice from sympy import factorint def A235991_gen(startvalue=0): # generator of terms >= startvalue return filter(lambda n: n&3==2 or (n&1 and sum(factorint(n).values())&1), count(max(startvalue, 0))) A235991_list = list(islice(A235991_gen(), 40)) # Chai Wah Wu, Nov 04 2022 CROSSREFS Cf. A003415, A006519, A007814, A165560, A235992 (complement), A000040 (subsequence). Sequence in context: A345297 A336533 A359782 * A327906 A333866 A325362 Adjacent sequences: A235988 A235989 A235990 * A235992 A235993 A235994 KEYWORD nonn AUTHOR Reinhard Zumkeller, Mar 11 2014 STATUS approved

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Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)