cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A224987 Numbers such that Liouville's function (A002819) and the little omega analog to Liouville's function (A174863) are equal.

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%I A224987 #14 Jul 10 2015 19:25:10
%S A224987 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 A224987 13092,13093,13094,13095,13096,13097,13098,13099,13100,13101,13102,
%U A224987 13103,13104,13105,13106,13107,13232,13233,13234,13235,13239,13240,13241,13242
%N A224987 Numbers such that Liouville's function (A002819) and the little omega analog to Liouville's function (A174863) are equal.
%C A224987 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 A224987 Donovan Johnson, <a href="/A224987/b224987.txt">Table of n, a(n) for n = 1..9056</a>
%e A224987 n = 43:
%e A224987 A002819(n) = sum_{k = 1..n} (-1)^bigomega(k) = -3.
%e A224987 A174863(n) = sum_{k = 1..n} (-1)^omega(k) = -3.
%e A224987 A002819(43) = A174863(43) = -3.
%t A224987 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 A224987 (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 A224987 Cf. A001221, A001222, A008836, A002819, A174863.
%K A224987 nonn
%O A224987 1,2
%A A224987 _Donovan Johnson_, Apr 22 2013