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A131384 Product of the digital sums of n for all the bases 2 to n (a 'digital-sum factorial'). 3
1, 1, 2, 2, 12, 24, 216, 192, 720, 3840, 97200, 69120, 2721600, 14515200, 130636800, 30965760, 3810240000, 3762339840, 384072192000, 445906944000, 10184771520000, 123605404876800, 12674382336000000, 2542739757465600 (list; graph; refs; listen; history; text; internal format)
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) = {p = n; for (b=2, n, digs = digits(n, b); p *= sum(k=1, #digs, digs[k]); ); return (p); } \\ Michel Marcus, Jul 15 2013

CROSSREFS

Cf. A131383.

Sequence in context: A164961 A122007 A137782 * A052612 A130306 A199127

Adjacent sequences:  A131381 A131382 A131383 * A131385 A131386 A131387

KEYWORD

nonn,base

AUTHOR

Hieronymus Fischer, Jul 05 2007

STATUS

approved

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Last modified April 27 10:54 EDT 2017. Contains 285512 sequences.