A352012
a(n) = Sum_{p|n, p prime} (n-1)!/(p-1)!.
Original entry on oeis.org
0, 1, 1, 6, 1, 180, 1, 5040, 20160, 378000, 1, 59875200, 1, 6235669440, 47221574400, 1307674368000, 1, 533531142144000, 1, 126713646259200000, 1219830034655232000, 51090956251003468800, 1, 38778025108327464960000, 25852016738884976640000
Offset: 1
-
f:= proc(n) local p;
add( (n-1)!/(p-1)!, p = numtheory:-factorset(n))
end proc:
map(f, [$1..30]): # Robert Israel, Nov 14 2024
-
a[1] = 0; a[n_] := (n - 1)! * Plus @@ (1/(FactorInteger[n][[;; , 1]] - 1)!); Array[a, 25] (* Amiram Eldar, Mar 01 2022 *)
-
a(n) = sumdiv(n, d, isprime(d)*(n-1)!/(d-1)!);
-
my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(-sum(k=1, N, isprime(k)*log(1-x^k)/k!))))
-
a(n) = my(f=factor(n)); sum(k=1, #f~, (n-1)!/(f[k,1]-1)!); \\ Michel Marcus, Mar 01 2022
A352013
a(n) = Sum_{d|n} (-1)^(n/d+1) * (n-1)!/(d-1)!.
Original entry on oeis.org
1, 0, 3, -11, 25, -59, 721, -10919, 60481, -15119, 3628801, -93471839, 479001601, -8648639, 134399865601, -2833553923199, 20922789888001, -174888473759999, 6402373705728001, -228084898487846399, 3652732042831872001, -14079294028799
Offset: 1
-
restart;
f:= proc(n) local d;
add((-1)^(n/d + 1) * (n-1)!/(d-1)!, d = numtheory:-divisors(n))
end proc:
map(f, [$1..30]); # Robert Israel, Nov 14 2024
-
a[n_] := DivisorSum[n, (-1)^(n/#+1) * (n-1)!/(#-1)! &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)
-
a(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
-
my(N=40, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)))
A352005
Expansion of e.g.f. Product_{k>=1} (1 + x^prime(k))^(1/prime(k)!).
Original entry on oeis.org
1, 0, 1, 1, -3, 11, -5, -83, -2919, 18838, 118371, 583826, -27365327, -12780260, 405396069, 32646641041, -232690739007, 4816360930145, -46984166770283, -541620811734953, -49355727191815599, 907100235094018036, 10877428540752188625, 139350853273096742762
Offset: 0
-
my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(isprime(k)/k!))))
-
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, isprime(d)*(-1)^(k/d+1)*(k-1)!/(d-1)!)*x^k/k!))))
Showing 1-3 of 3 results.