A358280
a(n) = Sum_{d|n} (d-1)!.
Original entry on oeis.org
1, 2, 3, 8, 25, 124, 721, 5048, 40323, 362906, 3628801, 39916930, 479001601, 6227021522, 87178291227, 1307674373048, 20922789888001, 355687428136444, 6402373705728001, 121645100409194912, 2432902008176640723, 51090942171713068802, 1124000727777607680001
Offset: 1
-
a[n_] := DivisorSum[n, (# - 1)! &]; Array[a, 23] (* Amiram Eldar, Aug 30 2023 *)
-
a(n) = sumdiv(n, d, (d-1)!);
-
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, (k-1)!*x^k/(1-x^k)))
A355888
a(n) = Sum_{k=1..n} k! * floor(n/k).
Original entry on oeis.org
1, 4, 11, 38, 159, 888, 5929, 46276, 409163, 4038086, 43954887, 522957240, 6749978041, 93928274284, 1401602642411, 22324392570758, 378011820666759, 6780385526758368, 128425485935590369, 2561327494115859316, 53652269665825304363, 1177652997443472901166
Offset: 1
-
Table[Sum[k!*Floor[n/k], {k,1,n}], {n,1,25}] (* Vaclav Kotesovec, Aug 11 2025 *)
-
a(n) = sum(k=1, n, n\k*k!);
-
a(n) = sum(k=1, n, sumdiv(k, d, d!));
-
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-x^k))/(1-x))
-
from math import factorial
def A355888(n): return factorial(n)+n+sum(factorial(k)*(n//k) for k in range(2,n)) if n>1 else 1 # Chai Wah Wu, Jul 21 2022
A358279
a(n) = Sum_{d|n} (d-1)! * d^(n/d).
Original entry on oeis.org
1, 3, 7, 29, 121, 747, 5041, 40433, 362935, 3629433, 39916801, 479006531, 6227020801, 87178326609, 1307674371487, 20922790212353, 355687428096001, 6402373709021811, 121645100408832001, 2432902008212950169, 51090942171709691335, 1124000727778046766849
Offset: 1
-
a[n_] := DivisorSum[n, (# - 1)! * #^(n/#) &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)
-
a(n) = sumdiv(n, d, (d-1)!*d^(n/d));
-
my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-k*x^k)))
A351710
a(n) = Sum_{p|n, p prime} (n-p)!.
Original entry on oeis.org
0, 1, 1, 2, 1, 30, 1, 720, 720, 40440, 1, 3991680, 1, 479006640, 482630400, 87178291200, 1, 22230464256000, 1, 6403681380096000, 6402460884019200, 2432902008216556800, 1, 1175091669949317120000, 2432902008176640000, 620448401733245666380800, 620448401733239439360000
Offset: 1
a(6) = 30; a(6) = Sum_{p|6} (6-p)! = (6-2)! + (6-3)! = 4*3*2*1 + 3*2*1 = 30.