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 A030230 Numbers that have an odd number of distinct prime divisors. 19
 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 42, 43, 47, 49, 53, 59, 60, 61, 64, 66, 67, 70, 71, 73, 78, 79, 81, 83, 84, 89, 90, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 120, 121, 125, 126, 127, 128, 130, 131, 132, 137, 138, 139, 140, 149 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 H. Helfgott and A. Ubis, Primos, paridad y análisis, arXiv:1812.08707 [math.NT], Dec. 2018. FORMULA From Benoit Cloitre, Dec 08 2002: (Start) k such that Sum_{d|k} mu(d)*tau(d) = (-1)^omega(k) = -1 where mu(d) = A008683(d), tau(d) = A000005(d) and omega(d) = A001221(d). k such that A023900(k) < 0. (End) gcd(A008472(a(n)), A007947(a(n))) > 1; see A014963. - Labos Elemer, Mar 26 2003 A076479(a(n)) = -1. - Reinhard Zumkeller, Jun 01 2013 MAPLE q:= n-> is(nops(ifactors(n)[2])::odd): select(q, [\$1..150])[]; # Alois P. Heinz, Feb 12 2021 MATHEMATICA (* Prior to version 7.0 *) littleOmega[n_] := Length[FactorInteger[n]]; Select[ Range[2, 149], (-1)^littleOmega[#] == -1 &] (* Jean-François Alcover, Nov 30 2011, after Benoit Cloitre *) (* Version 7.0+ *) Select[Range[2, 149], (-1)^PrimeNu[#] == -1 &] Select[Range[1000], OddQ[PrimeNu[#]]&] (* Harvey P. Dale, Nov 27 2012 *) PROG (Haskell) a030230 n = a030230_list !! (n-1) a030230_list = filter (odd . a001221) [1..] -- Reinhard Zumkeller, Aug 14 2011 (PARI) is(n)=omega(n)%2 \\ Charles R Greathouse IV, Sep 14 2015 CROSSREFS Cf. A030231, A123066. Cf. A008472, A007947, A014963. Cf. A076479. Cf. A008683, A000005, A001221, A023900. Sequence in context: A331912 A326848 A328957 * A089352 A086486 A071139 Adjacent sequences: A030227 A030228 A030229 * A030231 A030232 A030233 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified February 7 15:16 EST 2023. Contains 360127 sequences. (Running on oeis4.)