A139465 Number of distinct prime factors of n! + 2n - 1.

1, 1, 1, 1, 2, 2, 2, 3, 1, 1, 5, 2, 3, 4, 2, 2, 3, 4, 3, 3, 3, 3, 4, 2, 5, 4, 2, 6, 6, 2, 4, 5, 5, 3, 3, 3, 2, 5, 5, 4, 5, 2, 5, 5, 5, 5, 8, 8, 5, 6, 4, 2, 7, 5, 5, 6, 4, 5, 3, 8, 7, 6, 5, 7, 4, 3, 5, 6, 1, 1, 7, 5, 8, 7, 3, 1, 4, 4, 5, 5, 4, 2, 4, 5, 5, 7, 3, 6, 7, 7, 4, 7, 6, 5, 7, 5, 3, 8, 5, 3, 4, 6, 5, 7, 7

Offset

1,5

Links

Sean A. Irvine, Table of n, a(n) for n = 1..118

Florian Luca and Igor E. Shparlinski, On the largest prime factor of n! + 2^n - 1, Journal de Théorie des Nombres de Bordeaux 17 (2005), 859-870.

Apurva Rai, Python Program for a(81)-a(100)

Apurva Rai, Python program for a(101)-a(105)

Formula

a(n) = A001221(A139464(n)). - Amiram Eldar, Feb 05 2020

Mathematica

a = {}; Do[AppendTo[a, n! + 2 n - 1], {n, 1, 40}]; b = {}; Do[c = Length[FactorInteger[a[[n]]]]; AppendTo[b, c], {n, 1, Length[a]}]; b (* Artur Jasinski *)
PrimeNu @ Table[n! + 2*n - 1, {n, 1, 30}] (* Amiram Eldar, Feb 05 2020 *)

Prog

(PARI) a(n)=omega(n!+2*n-1) \\ Charles R Greathouse IV, Feb 01 2013

Crossrefs

Cf. A001221, A127986, A127987, A139023, A139024, A139464, A139466, A139467.

Sequence in context: A198862 A349227 A264025 * A010244 A141298 A256915

Adjacent sequences: A139462 A139463 A139464 * A139466 A139467 A139468

Keyword

nonn

Author

Artur Jasinski, Apr 22 2008

Extensions

a(41)-a(60) from Amiram Eldar, Feb 05 2020

a(61)-a(80) from Jinyuan Wang, Apr 03 2020

a(81)-a(100) from Apurva Rai, Sep 20 2020

a(101)-a(105) from Apurva Rai, Sep 21 2020

Status

approved