A054991 -id:A054991 - cp's OEIS frontend

A193295 Number of prime divisors (with multiplicity) of n^2 - 1.

1, 3, 2, 4, 2, 5, 3, 5, 3, 5, 2, 5, 3, 6, 3, 7, 2, 6, 3, 5, 3, 6, 3, 6, 5, 5, 4, 6, 2, 8, 3, 7, 4, 6, 3, 6, 3, 6, 3, 7, 2, 6, 4, 5, 4, 7, 3, 8, 4, 6, 3, 7, 3, 8, 4, 6, 3, 6, 2, 6, 4, 8, 5, 9, 3, 6, 3, 6, 3, 8, 2, 7, 4, 5, 5, 6, 3, 8, 5, 7, 5, 6, 3, 6, 4, 6

Offset: 2

Vladimir Joseph Stephan Orlovsky, Jul 22 2011

nonn

T. D. Noe, Table of n, a(n) for n = 2..10000

Cf. A046051, A054992, A054990, A054991, A082863.

Table[PrimeOmega[n^2 - 1], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)

a(n)=bigomega(n^2-1) \\ Charles R Greathouse IV, Jul 30 2011

A336418 Numbers with a factorial number of divisors.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 28, 29, 31, 32, 37, 41, 43, 44, 45, 47, 50, 52, 53, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 83, 89, 92, 97, 98, 99, 101, 103, 107, 109, 113, 116, 117, 124, 127, 131, 137, 139, 147, 148, 149, 151, 153, 157, 163

Offset: 1

Gus Wiseman, Jul 27 2020

nonn

Positive integers n such that A000005(n) belongs to A000142.

A000005 counts divisors.
A048656 counts squarefree divisors of n!.
A325617 counts permutations of the multiset of prime factors of n!.
A336414 counts divisors of n! with distinct prime exponents.
Cf. A000142, A001221, A001222, A002982, A007489, A022559, A027423, A032741, A054991, A090630, A108731, A181796, A251753, A336416.

nn=5;Select[Range[nn!],MemberQ[Array[Factorial,nn],Length[Divisors[#]]]&]

A064186 Numbers n such that n!+1 and n!-1 have the same number of prime divisors (with repetition).

Original entry on oeis.org

3, 5, 8, 9, 10, 13, 17, 20, 22, 24, 26, 34, 39, 53, 59, 61, 63, 69, 70, 76, 80, 87, 97, 99, 103, 124, 130

Offset: 1

Jason Earls, Sep 20 2001

200, 236, 392 and 634 are terms. - Chai Wah Wu, Jan 03 2020

Cf. A054990, A054991.

Select[Range[30], PrimeOmega[#! - 1] == PrimeOmega[#! + 1] &] (* Amiram Eldar, Dec 01 2019 *)

for(n=2,100, if(bigomega(n!+1)==bigomega(n!-1),print(n)))

a(15)-a(25) from Donovan Johnson, Mar 09 2008
Offset corrected by Donovan Johnson, Jul 11 2013
a(26)-a(27) from Amiram Eldar, Dec 01 2019

cp's OEIS Frontend

A193295 Number of prime divisors (with multiplicity) of n^2 - 1.

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A336418 Numbers with a factorial number of divisors.

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A064186 Numbers n such that n!+1 and n!-1 have the same number of prime divisors (with repetition).

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