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A026424
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Number of prime divisors (counted with multiplicity) is odd; Liouville function lambda(n) (A008836) is negative.
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197
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2, 3, 5, 7, 8, 11, 12, 13, 17, 18, 19, 20, 23, 27, 28, 29, 30, 31, 32, 37, 41, 42, 43, 44, 45, 47, 48, 50, 52, 53, 59, 61, 63, 66, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 83, 89, 92, 97, 98, 99, 101, 102, 103, 105, 107, 108, 109, 110, 112
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OFFSET
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1,1
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COMMENTS
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Lexicographically earliest sequence of distinct nonnegative integers with no term being the product of any two not necessarily distinct terms. The equivalent sequence for addition/subtraction is A005408 (the odd numbers), for exponentiation is A259444, and for binary exclusive OR is A000069. - Peter Munn, Mar 16 2018
The equivalent lexicographically earliest sequence with no term being the product of any two distinct terms is A026416. A000028 is similarly the equivalent sequence when A059897 is used as multiplicative operator in place of standard integer multiplication. - Peter Munn, Mar 16 2019
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LINKS
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S. Ramanujan, Irregular numbers, J. Indian Math. Soc., 5 (1913), 105-106; Coll. Papers 20-21.
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FORMULA
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Sum 1/a(n)^m = (zeta(m)^2-zeta(2m))/(2*zeta(m)), Dirichlet g.f. of A066829. - Ramanujan.
n>=2 is in sequence if n is not the product of two smaller elements. - David W. Wilson, May 06 2005
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MAPLE
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isA026424 := proc(n)
if type(numtheory[bigomega](n) , 'odd') then
true;
else
false;
end if;
end proc:
option remember;
if n =1 then
2;
else
for a from procname(n-1)+1 do
if isA026424(a) then
return a;
end if;
end do:
end if;
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MATHEMATICA
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Select[Range[2, 112], OddQ[Total[FactorInteger[#]][[2]]] &] (* T. D. Noe, May 07 2011 *)
(* From version 7 on *) Select[Range[2, 112], LiouvilleLambda[#] == -1 &] (* Jean-François Alcover, Aug 19 2013 *)
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PROG
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(Haskell)
a026424 n = a026424_list !! (n-1)
a026424_list = filter (odd . a001222) [1..]
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CROSSREFS
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Apart from initial term, same as A026422.
Cf. A026416 and cross-references therein.
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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