A038048
a(n) = (n-1)! * sigma(n).
Original entry on oeis.org
1, 3, 8, 42, 144, 1440, 5760, 75600, 524160, 6531840, 43545600, 1117670400, 6706022400, 149448499200, 2092278988800, 40537905408000, 376610217984000, 13871809695744000, 128047474114560000, 5109094217170944000
Offset: 1
a(6) = 5! * (1 + 2 + 3 + 6) = 1440 = 6! * (1 + 1/2 + 1/3 + 1/6).
- F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 56 (1.4.67).
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159, #10, A(n,1).
- T. D. Noe, Table of n, a(n) for n = 1..100
- Xiaojun Liu, Motohico Mulase, Adam Sorkin, Quantum curves for simple Hurwitz numbers of an arbitrary base curve, arXiv:1304.0015 [math.AG], 2013.
- H. Ochiai, Counting functions for branched covers of elliptic curves and quasi-modular forms, arXiv:math-ph/9909023, 1999.
-
a := n -> n!*add(1/j, j=numtheory:-divisors(n)): seq(a(n), n=1..23); # Emeric Deutsch, Jul 24 2005
-
a[n_] := (n-1)!*DivisorSigma[1, n]; Table[a[n], {n, 20}] (* Jean-François Alcover, Mar 23 2011 *)
-
a(n)=(n-1)!*sigma(n) \\ Charles R Greathouse IV, Mar 09 2014
-
A038048 = lambda n: factorial(n-1)*sigma(n,1)
[A038048(n) for n in (1..20)] # Peter Luschny, Jan 19 2016
A110374
a(n) = Sum_{composite c <= n} n!/c.
Original entry on oeis.org
6, 30, 300, 2100, 21840, 236880, 2731680, 30048480, 400498560, 5206481280, 79117758720, 1273944672000, 21690789120000, 368743415040000, 6993068898816000, 132868309077504000, 2779011281958912000, 60792138929313792000, 1388517998616612864000
Offset: 4
a(8) = 8! * (1/4 + 1/6 + 1/8) = 21840.
-
a:=proc(n) local s,i :s:=0: for i from 4 to n do if isprime(i)=false then s:=s+1/i else s:=s: fi od: n!*s; end; seq(a(n),n=4..23); # Emeric Deutsch, Jul 24 2005
-
from sympy import factorial, isprime, Rational
def a(n): return factorial(n) * sum(Rational(1, c) for c in range(4, n+1) if not isprime(c))
print([a(n) for n in range(4, 23)]) # Michael S. Branicky, Jun 30 2021
A110376
a(n) = Sum_{r < n, gcd(r,n)=1} n!/r.
Original entry on oeis.org
1, 2, 9, 32, 250, 864, 12348, 67584, 804816, 5760000, 116915040, 686776320, 19323757440, 157991178240, 2951575200000, 42301705420800, 1202482800691200, 10048607738265600, 425162773111910400, 4541227794432000000
Offset: 1
a(6) = 6!(1/1 + 1/5) = 864.
-
a:=proc(n) local s,r: s:=0: for r from 1 to n do if gcd(r,n)=1 then s:=s+1/r else s:=s: fi: od: n!*s end: seq(a(n),n=1..23); # Emeric Deutsch, Jul 25 2005
-
Do[Print[n! * Plus @@ Map[(1/#)&, Select[Range[n], GCD[ #, n] == 1 &]]], {n, 1, 30}] (* Ryan Propper, Jul 25 2005 *)
A110377
a(n) = Sum_{r < n, gcd(r,n)=1} n!/r!.
Original entry on oeis.org
1, 2, 9, 28, 205, 726, 8659, 47384, 562545, 4234330, 68588311, 483088332, 10699776685, 102434734598, 2016289908585, 24588487650736, 611171244308689, 6456997293606738, 209020565553571999, 2838875160624256460
Offset: 1
a(6) = 6!(1/1! + 1/5!) = 726.
-
a:=proc(n) local s,r: s:=0: for r from 1 to n do if gcd(r,n)=1 then s:=s+1/r! else s:=s: fi: od: n!*s end: seq(a(n),n=1..23); # Emeric Deutsch, Jul 25 2005
A110378
a(n) = Sum_{prime p <= n} n!/p!.
Original entry on oeis.org
1, 4, 16, 81, 486, 3403, 27224, 245016, 2450160, 26951761, 323421132, 4204474717, 58862646038, 882939690570, 14127035049120, 240159595835041, 4322872725030738, 82134581775584023, 1642691635511680460
Offset: 2
a(6) = 6!(2! + 1/3! + 1/5!) = 486.
-
a:=proc(n) local s, i: s:=0: for i from 2 to n do if isprime(i)=true then s:=s+1/i! else s:=s: fi: od: n!*s: end: seq(a(n),n=2..23); # Emeric Deutsch, Jul 24 2005
A110379
a(n) = Sum_{composite c <= n} n!/c!.
Original entry on oeis.org
1, 5, 31, 217, 1737, 15634, 156341, 1719751, 20637013, 268281169, 3755936367, 56339045506, 901424728097, 15324220377649, 275835966797683, 5240883369155977, 104817667383119541, 2201171015045510362
Offset: 4
a(6) = 6!(1/4! + 1/6!) = 31.
-
a:=proc(n) local s,i :s:=0: for i from 4 to n do if isprime(i)=false then s:=s+1/i! else s:=s: fi od: n!*s; end; seq(a(n),n=4..24); # Emeric Deutsch, Jul 25 2005
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