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 1-6 of 6 results.

A062959 Number of divisors of n^(n!) (A053986).

Original entry on oeis.org

1, 3, 7, 49, 121, 519841, 5041, 120961, 725761, 13168196697601, 39916801, 458885067042124801, 6227020801, 7600054456726354022401, 1710012252726814772736001, 83691159552001, 355687428096001, 81980778135594585487141085184001, 121645100408832001
Offset: 1

Views

Author

Jason Earls, Jul 22 2001

Keywords

Crossrefs

Programs

  • Maple
    a:= n-> mul(n!*i[2]+1, i=ifactors(n)[2]):
    seq (a(n), n=1..20);  # Alois P. Heinz, Dec 17 2011
  • PARI
    for(n=1,13,print(numdiv(n^(n!))))

Extensions

More terms from Henry Bottomley, Jul 24 2001
More terms from Alois P. Heinz, Dec 17 2011

A187751 a(n) = n^(n!) mod (n!)^n.

Original entry on oeis.org

0, 0, 0, 81, 225280, 7991790625, 1078848154238976, 65180706714634067542224001, 1650157594512930366268925848349310976, 66807065275536807794426016376688705273224158387201, 228020326859403543540241849077865865705999564800000000000000000000
Offset: 0

Views

Author

Alex Ratushnyak, Jan 03 2013

Keywords

Examples

			a(3) = 3^6 mod 6^3 = 729 mod 216 = 81.
		

Crossrefs

Programs

  • Maxima
    A187751(n):=mod(n^(n!),(n!)^n)$ makelist(A187751(n),n,0,9); /* Martin Ettl, Jan 13 2013 */
  • Python
    import math
    for n in range(12):
      f = math.factorial(n)
      print(pow(n, f, f**n))
    

Formula

a(n) = A053986(n) mod A036740(n).

Extensions

a(10) from David Radcliffe, Jul 05 2025

A202336 Number of digits in n^(n!).

Original entry on oeis.org

1, 1, 1, 3, 15, 84, 561, 4260, 36413, 346276, 3628801, 41569064, 516929544, 6936548425, 99917483647, 1537944393896, 25193549397053, 437655212248536, 8036723680196724, 155554110186062367, 3165278489148945082, 67553429525569109411, 1508884070229326953381
Offset: 0

Views

Author

Jacques ALARDET, Dec 17 2011

Keywords

Examples

			a(3) = 3 because 3^3! = 729 with 3 digits;
a(4) = 15 because 4^4! = 281474976710656 with 15 digits.
		

Crossrefs

Programs

  • Maple
    a:= proc(n) local h;
          Digits:= 1000;
          1+ `if`(n=0, 0, floor(n!*simplify(log[10](n))))
        end:
    seq(a(n), n=0..30); # Alois P. Heinz, Dec 17 2011
  • Mathematica
    Table[IntegerLength[n^n!],{n,0,10}] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 19 2024 *)

Formula

a(n) = A055642(A053986(n)). - Michel Marcus, Aug 22 2013

Extensions

More terms from Alois P. Heinz, Dec 17 2011

A202358 Sum of digits of n^(n!).

Original entry on oeis.org

0, 1, 4, 18, 73, 334, 2592, 18919, 164476, 1558521, 1, 187044031, 2326111614, 31214008090
Offset: 0

Views

Author

Jacques ALARDET, Dec 17 2011

Keywords

Comments

a(10^k) = 1. - Chai Wah Wu, Dec 18 2019

Examples

			a(3) = 18 because 3^3! = 729 with digit sum 7+2+9 = 18.
		

Crossrefs

Programs

  • Maple
    ds:= proc(n) local r;
           `if`(n<10, n, ds(iquo(n, 10^iquo(length(n), 2), 'r'))+ds(r))
         end:
    a:= n-> ds(n^n!):
    seq(a(n), n=0..10);  # Alois P. Heinz, Dec 17 2011
  • Python
    from math import factorial
    def a(n): return sum(map(int, str(n**(factorial(n)))))
    print([a(n) for n in range(10)]) # Michael S. Branicky, Jan 28 2021

Formula

a(n) = A007953(A053986(n)). - Michel Marcus, Aug 22 2013

Extensions

a(11)-a(12) from Lars Blomberg, Jan 18 2013
a(13) from Chai Wah Wu, Oct 25 2021

A213065 a(n) = n^n! - n!^n.

Original entry on oeis.org

-1, 0, 0, 513, 281474976378880, 752316384526264005099991383822237233803945956334136013765601092018187046026142190625
Offset: 0

Views

Author

Pratik Jain, Jun 04 2012

Keywords

Comments

a(6) has 561 digits: 1.8573779... * 10^560.

Crossrefs

Programs

  • Mathematica
    Table[n^n! - n!^n, {n, 0, 4}] (* T. D. Noe, Jun 04 2012 *)
  • PARI
    a(n) = n^n! - n!^n \\ Stefano Spezia, Aug 02 2025

Extensions

a(5) from Stefano Spezia, Aug 02 2025

A307031 n to the power n double factorial, n^(n!!).

Original entry on oeis.org

1, 4, 27, 65536, 30517578125, 22452257707354557240087211123792674816, 54361846697263307560529495055267343940077014163990039113495978834700158362117849904436807
Offset: 1

Views

Author

Mark Stander, Mar 20 2019

Keywords

Comments

The next term -- a(8) -- has 347 digits. - Harvey P. Dale, Aug 11 2021

Crossrefs

Programs

  • Mathematica
    Table[n^n!!,{n,7}] (* Harvey P. Dale, Aug 11 2021 *)
  • Python
    def doublefactorial(n):
         if n <= 0:
             return 1
         else:
             return n * doublefactorial(n-2)
    for n in range(1,m):
        print(n**doublefactorial(n))

Formula

a(n) = n^(n!!).
Showing 1-6 of 6 results.