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

%I A131384 #30 Jun 13 2022 12:37:50
%S A131384 1,1,2,2,12,24,216,192,720,3840,97200,69120,2721600,14515200,
%T A131384 130636800,30965760,3810240000,3762339840,384072192000,445906944000,
%U A131384 10184771520000,123605404876800,12674382336000000,2542739757465600
%N A131384 Product of the digital sums of n for all the bases 2 to n (a 'digital-sum factorial').
%C A131384 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
%H A131384 Hieronymus Fischer, <a href="/A131384/b131384.txt">Table of n, a(n) for n = 1..200</a>
%F A131384 a(n) = Product_{p=2..n} ds_p(n) where ds_p = digital sum base p.
%F A131384 a(n) = Product_{p=2..n} (n-(p-1)*Sum_{k>0} floor(n/p^k)).
%F A131384 [Both formulas corrected in accordance with the changed definition by the author; Jul 19 2013]
%e A131384 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
%t A131384 Table[Times @@ Map[Total@ IntegerDigits[n, #] &, Range[2, n]], {n, 24}] (* _Michael De Vlieger_, Jan 03 2017 *)
%o A131384 (PARI) a(n) = prod(k=2, n, sumdigits(n,k)); \\ _Michel Marcus_, Jun 13 2022
%Y A131384 Cf. A131383.
%K A131384 nonn,base
%O A131384 1,3
%A A131384 _Hieronymus Fischer_, Jul 05 2007