A351709 -id:A351709 - cp's OEIS frontend

A351708 a(n) = Sum_{p|n, p prime} (n/p)!.

0, 1, 1, 2, 1, 8, 1, 24, 6, 122, 1, 744, 1, 5042, 126, 40320, 1, 363600, 1, 3628824, 5046, 39916802, 1, 479041920, 120, 6227020802, 362880, 87178291224, 1, 1307677997520, 1, 20922789888000, 39916806, 355687428096002, 5160, 6402374184729600, 1

Offset: 1

Wesley Ivan Hurt, Feb 16 2022

			a(6) = 8; a(6) = Sum_{p|6} (6/p)! = (6/2)! + (6/3)! = 3*2 + 2*1 = 8.

Robert Israel, Table of n, a(n) for n = 1..897

Cf. A000040, A000142, A062363, A351709.

f:= proc(n) local p;
  add((n/p)!, p = numtheory:-factorset(n))
end proc:
map(f, [$1..40]); # Robert Israel, Dec 05 2022

Table[DivisorSum[n, Factorial[n/#] &, PrimeQ], {n, 36}] (* Michael De Vlieger, Dec 06 2022 *)

a(A000040(n)) = 1.

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

Wesley Ivan Hurt, Feb 16 2022

nonn

			a(6) = 30; a(6) = Sum_{p|6} (6-p)! = (6-2)! + (6-3)! = 4*3*2*1 + 3*2*1 = 30.

Cf. A000040, A000142, A062363, A351708, A351709.

a(A000040(n)) = 1.

cp's OEIS Frontend

A351708 a(n) = Sum_{p|n, p prime} (n/p)!.

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