A145194 Least k for which Omega(6k-1) + Omega(6k+1) >= n.

1, 1, 4, 20, 41, 104, 479, 1146, 7603, 16521, 91146, 188021, 188021, 1861979, 14122396, 43294271, 203450521, 203450521, 5877278646, 5900065104, 16886393229

Offset

1,3

Comments

a(22) <= 170499674479. a(23) <= 1307169596354. a(24) <= 3178914388021. a(25) <= 3178914388021. a(26) <= 43614705403646 [From Donovan Johnson, Feb 17 2010]

Links

Table of n, a(n) for n=1..21.

Example

When k=1,2 and 3, Omega(6k-1) + Omega(6k+1) = 2. When k=4, Omega(6k-1) + Omega(6k+1) = 3, so a(3)=4.

Mathematica

Maxie=0; For[x=6, x<10000001, x+=6, S=0; T=0; For[k=1, k< Length[FactorInteger[x-1]]+1, k++, S+= FactorInteger[x-1][[k]][[2]]]; For[m=1, m< Length[FactorInteger[x+1]]+1, m++, T+= FactorInteger[x+1][[m]][[2]]]; If[S+T>Maxie, Print[x/6, " ", S+T]; Maxie=S+T]]

Crossrefs

Cf. A145193

Sequence in context: A072977 A341895 A163365 * A164924 A033579 A294630

Adjacent sequences: A145191 A145192 A145193 * A145195 A145196 A145197

Keyword

nonn

Author

Arran Fernandez, Oct 03 2008

Extensions

a(15)-a(21) from Donovan Johnson, Feb 17 2010

Status

approved