A260620 Arithmetic derivative of superfactorial(n).

0, 0, 1, 16, 912, 179712, 200724480, 1389079756800, 78810485096448000, 38096713995308236800000, 177372596340389981454336000000, 8666143442523657424202209689600000000, 5080543621153782266150614213475696640000000000

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..43

Formula

a(n) = A003415(A000178(n)).

Maple

b:= proc(n) option remember; `if`(n<2, 0,
       b(n-1)*n + n!*add(i[2]/i[1], i=ifactors(n)[2]))
    end:
s:= proc(n) option remember; `if`(n=0, 1, n!*s(n-1)) end:
a:= proc(n) option remember; `if`(n=0, 0,
       b(n)*s(n-1)+n!*a(n-1))
    end:
seq(a(n), n=0..15);  # Alois P. Heinz, Sep 18 2015

Mathematica

a[n_] := If[n<2, 0, With[{g = BarnesG[n+2]}, g Sum[{p, e} = pe; e/p, {pe, FactorInteger[g]}]]];
a /@ Range[0, 15] (* Jean-François Alcover, Nov 14 2020 *)

Prog

(Python 3.8+)
from math import prod, factorial
from collections import Counter
from sympy import factorint
def A260620(n):
    s = prod(factorial(i) for i in range(2, n+1))
    return sum(s*e//p for p, e in sum(((lambda x: Counter({k:x[k]*(n-m+1) for k in x}))(factorint(m)) for m in range(2, n+1)), start=Counter({2:0})).items()) if n > 1 else 0 # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A003415, A000178, A068311.

Sequence in context: A283946 A289707 A006089 * A290940 A173953 A211105

Adjacent sequences: A260617 A260618 A260619 * A260621 A260622 A260623

Keyword

nonn

Author

Matthew Campbell, Sep 18 2015

Extensions

More terms from Alois P. Heinz, Sep 18 2015

Status

approved