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A224987 Numbers such that Liouville's function (A002819) and the little omega analog to Liouville's function (A174863) are equal. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

LINKS

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

EXAMPLE

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.

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-Fran├žois Alcover, May 03 2013, after Pari *)

PROG

(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)))

CROSSREFS

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

Sequence in context: A279672 A089181 A028425 * A024630 A032809 A279180

Adjacent sequences:  A224984 A224985 A224986 * A224988 A224989 A224990

KEYWORD

nonn

AUTHOR

Donovan Johnson, Apr 22 2013

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)