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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
OFFSET
1,1
COMMENTS
A165560(a(n)) = 1; A003415(a(n)) mod 2 = 1;
A007814(a(n)) <= 1, A006519(a(n)) <= 2.
LINKS
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 11 2014
STATUS
approved