A131384 Product of the digital sums of n for all the bases 2 to n (a 'digital-sum factorial').

1, 1, 2, 2, 12, 24, 216, 192, 720, 3840, 97200, 69120, 2721600, 14515200, 130636800, 30965760, 3810240000, 3762339840, 384072192000, 445906944000, 10184771520000, 123605404876800, 12674382336000000, 2542739757465600

Offset

1,3

Comments

Definition changed to run from bases 2 to n instead of 1 to n, in order to reflect the sequence numbers, correctly. - suggested by Michel Marcus and changed by the author, Jul 19 2013

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..200

Formula

a(n) = Product_{p=2..n} ds_p(n) where ds_p = digital sum base p.

a(n) = Product_{p=2..n} (n-(p-1)*Sum_{k>0} floor(n/p^k)).

[Both formulas corrected in accordance with the changed definition by the author; Jul 19 2013]

Example

5 = 11111_1 = 101_2 = 12_3 = 11_4 = 10_5. Thus a(5) = ds_1(5)*ds_2(5)*ds_3(5)*ds_4(5)*ds_5(5) = 5*2*3*2*1 = 60. - Michel Marcus, Jul 15 2013

Mathematica

Table[Times @@ Map[Total@ IntegerDigits[n, #] &, Range[2, n]], {n, 24}] (* Michael De Vlieger, Jan 03 2017 *)

Prog

(PARI) a(n) = prod(k=2, n, sumdigits(n, k)); \\ Michel Marcus, Jun 13 2022

Crossrefs

Cf. A131383.

Sequence in context: A122007 A365643 A137782 * A052612 A287951 A287629

Adjacent sequences: A131381 A131382 A131383 * A131385 A131386 A131387

Keyword

nonn,base

Author

Hieronymus Fischer, Jul 05 2007

Status

approved