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

1, 2, 3, 20, 21, 22, 23, 24, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 13092, 13093, 13094, 13095, 13096, 13097, 13098, 13099, 13100, 13101, 13102, 13103, 13104, 13105, 13106, 13107, 13232, 13233, 13234, 13235, 13239, 13240, 13241, 13242

Offset: 1

Author

Donovan Johnson, Apr 22 2013

Keywords

• nonn

Comments

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).

Examples

			n = 43:
A002819(n) = sum_{k = 1..n} (-1)^bigomega(k) = -3.
A174863(n) = sum_{k = 1..n} (-1)^omega(k) = -3.
A002819(43) = A174863(43) = -3.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..9056

Crossrefs

Cf. A001221, A001222, A008836, A002819, A174863.

Programs

Mathematica

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 *)

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)))