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

Author

Hieronymus Fischer, Jul 05 2007

Keywords

• nonn
• base

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

Examples

			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
		

Links

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

Crossrefs

Cf. A131383.

Programs

Mathematica

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

PARI

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

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]