A240023 Product of factorials of prime divisors of n (with multiplicity).

1, 2, 6, 4, 120, 12, 5040, 8, 36, 240, 39916800, 24, 6227020800, 10080, 720, 16, 355687428096000, 72, 121645100408832000, 480, 30240, 79833600, 25852016738884976640000, 48, 14400, 12454041600, 216, 20160, 8841761993739701954543616000000, 1440

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..300

Index to divisibility sequences.

Formula

Completely multiplicative with a(p) = p!.

Sum_{n>=1} 1/a(n) = 1/Product_{p prime} (1 - 1/p!) = 2.42064841562992124691... . - Amiram Eldar, Dec 24 2022

Maple

a:= n-> mul(i[1]!^i[2], i=ifactors(n)[2]):
seq(a(n), n=1..30);  # Alois P. Heinz, Mar 30 2014

Mathematica

f[p_, e_] := p!^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Aug 04 2022 *)

Prog

(PARI) a(n)=local(fm=factor(n)); prod(k=1, matsize(fm)[1], fm[k, 1]!^fm[k, 2])

Crossrefs

Cf. A000142.

Sequence in context: A210420 A306585 A118138 * A004583 A348720 A356476

Adjacent sequences: A240020 A240021 A240022 * A240024 A240025 A240026

Keyword

nonn,mult

Author

Franklin T. Adams-Watters, Mar 30 2014

Status

approved