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.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

Views

Author

Arran Fernandez, Oct 03 2008

Keywords

Comments

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

Examples

			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.

Crossrefs

Cf. A145193

Programs

  • 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]]

Extensions

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

A172155 a(n) = Omega(6*n-1)*Omega(6*n+1).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 4, 3, 2, 1, 4, 1, 2, 2, 2, 3, 1, 4, 1, 1, 4, 2, 4, 2, 1, 2, 1, 6, 2, 2, 2, 1, 3, 1, 4, 2, 4, 2, 1, 2, 6, 2, 2, 6, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 1, 6, 1, 2, 2, 2, 3, 1, 2, 6, 2, 2, 2, 2, 2, 2, 4, 1, 4, 4, 3, 2, 4, 2, 2, 1, 3, 4, 2, 3, 1, 3, 2, 1, 8, 2
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 26 2010

Keywords

Examples

			For n=1, Omega(6*n-1)*Omega(6*n+1)=Omega(5)*Omega(7)=1, so a(1)=1.

Crossrefs

Cf. A145193.

Programs

  • Maple
    A172155 := proc(n) numtheory[bigomega](6*n-1)*numtheory[bigomega](6*n+1) ; end proc: seq(A172155(n),n=1..100) ; # R. J. Mathar, Jan 30 2010
  • Mathematica
    Table[Times@@PrimeOmega[6*n+{1,-1}],{n,120}] (* Harvey P. Dale, Jul 16 2020 *)

Extensions

Corrected by R. J. Mathar, Jan 30 2010
Showing 1-2 of 2 results.

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