A139464 -id:A139464

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A139465

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

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.

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

A139466

Smallest prime factor of n! + 2n - 1.

+10
4

2, 5, 11, 31, 3, 17, 31, 3, 362897, 3628819, 3, 251, 5, 3, 93407, 200989, 3, 5, 211, 3, 199, 38189, 3, 314707, 7, 3, 2473, 5, 3, 98274048659069, 1447, 3, 5, 585341, 3, 61, 8150209692797, 3, 7, 131, 3, 193, 5, 3, 73, 7, 3, 5, 53, 3, 647, 151897, 3, 67801, 7001

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Apurva Rai, Table of n, a(n) for n = 1..105 (terms n = 1..60 from Amiram Eldar)

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

Apurva Rai, Python program to test a(61)-a(105)

FORMULA

a(n) = A020639(A139464(n)). - Amiram Eldar, Feb 05 2020

MATHEMATICA

a = {}; Do[AppendTo[a, n! + 2 n - 1], {n, 1, 40}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[1]]; AppendTo[b, d[[1]]], {n, 1, Length[a]}]; b (* Artur Jasinski *)

FactorInteger[#][[1, 1]] & /@ Table[n! + 2*n - 1, {n, 1, 18}] (* Amiram Eldar, Feb 05 2020 *)

PROG

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

CROSSREFS

Cf. A020639, A127986, A127987, A139023, A139024, A139464, A139465, A139467.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 22 2008

EXTENSIONS

a(41)-a(55) from Amiram Eldar, Feb 05 2020

STATUS

approved

A139467

Largest prime factor of n! + 2n - 1.

+10
4

2, 5, 11, 31, 43, 43, 163, 2689, 362897, 3628819, 179, 1908373, 800903, 101341, 13999747, 104099179, 10778406912001, 1300448327, 356961701, 62382102773760001, 10367823077693, 11437176299, 102338720137, 1971511284252461621, 4324853339, 25264139643338071514377, 4403101273925738843820461

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Robert Israel and Amiram Eldar, Table of n, a(n) for n = 1..60 (terms 1..57 from Robert Israel)

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

FORMULA

a(n) = A006530(A139464(n)). - Amiram Eldar, Feb 05 2020

MAPLE

seq(max(numtheory:-factorset(n!+2*n-1)), n=1..30); # Robert Israel, Jun 28 2018

MATHEMATICA

a = {}; Do[k = n! + 2 n - 1; c = First[Last[FactorInteger[k]]]; AppendTo[a, c], {n, 1, 40}]; a (*Artur Jasinski*)

Table[FactorInteger[n!+2n-1][[-1, 1]], {n, 30}] (* Harvey P. Dale, Aug 31 2011 *)

PROG

(PARI) a(n)=my(f=factor(n!+2*n-1)[, 1]); f[#f] \\ Charles R Greathouse IV, Feb 01 2013

CROSSREFS

Cf. A006530, A127986, A127987, A139023, A139024, A139464, A139465, A139466.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 22 2008

EXTENSIONS

More terms from Robert Israel, Jun 28 2018

STATUS

approved

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