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%I #14 Jul 10 2015 19:25:10
%S 1,2,3,20,21,22,23,24,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
%T 13092,13093,13094,13095,13096,13097,13098,13099,13100,13101,13102,
%U 13103,13104,13105,13106,13107,13232,13233,13234,13235,13239,13240,13241,13242
%N Numbers such that Liouville's function (A002819) and the little omega analog to Liouville's function (A174863) are equal.
%C Numbers n such that A002819(n) = A174863(n). There are 9056 terms <= 10^12 (the largest is 16959554). For n from 16959555 to 10^12, A002819(n) < A174863(n).
%H Donovan Johnson, <a href="/A224987/b224987.txt">Table of n, a(n) for n = 1..9056</a>
%e n = 43:
%e A002819(n) = sum_{k = 1..n} (-1)^bigomega(k) = -3.
%e A174863(n) = sum_{k = 1..n} (-1)^omega(k) = -3.
%e A002819(43) = A174863(43) = -3.
%t PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; PrimeNu[n_] := Length[FactorInteger[n]]; Reap[For[s1 = 0; s2 = 0; n = 1, n < 15000, n++, s1 = s1 + (-1)^PrimeOmega[n]; s2 = s2 + (-1)^PrimeNu[n]; If[s1 == s2, Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, May 03 2013, after Pari *)
%o (PARI) s1=0; s2=0; c=0; for(n=1, 16959554, s1=s1+(-1)^bigomega(n); s2=s2+(-1)^omega(n); if(s1==s2, c++; write("b224987.txt", c " " n)))
%Y Cf. A001221, A001222, A008836, A002819, A174863.
%K nonn
%O 1,2
%A _Donovan Johnson_, Apr 22 2013
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