%I A007954
%S A007954 0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,2,4,6,8,10,12,14,16,18,0,3,
               6,9,12,15,18,21,24,27,0,
%T A007954 4,8,12,16,20,24,28,32,36,0,5,10,15,20,25,30,35,40,45,0,6,12,18,24,30,
               36,42,48,54,0,7,14,21,28,
%U A007954 35,42,49,56,63,0,8,16,24,32,40,48,56,64,72,0,9,18,27,36,45,54,63,72,81,
               0,0,0,0,0,0,0,0
%N A007954 Product of digits of n.
%C A007954 A000035(a(A014261(n))) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 30 2007
%C A007954 Moebius transform of A093811(n). a(n) = A093811(n) * A008683(n), where 
               operation * denotes Dirichlet convolution for n >= 1. Dirichlet convolution 
               of functions b(n), c(n) is function a(n) = b(n) * c(n) = Sum_{d|n} 
               b(d)*c(n/d). Simultaneously holds Dirichlet multiplication: a(n) 
               * A000012(n) = A093811(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Mar 22 2009]
%D A007954 F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 
               1993
%H A007954 N. J. A. Sloane, <a href="b007954.txt">Table of n, a(n) for n = 0..10000</
               a>
%H A007954 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A007954 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>.
%p A007954 A007954 := proc(n) local t1,t2; t1 := n; t2 := 1; while t1 <> 0 do t2 
               := t2 * (t1 mod 10); t1 := floor(t1/10); od: t2; end;
%t A007954 Array[ Times @@ IntegerDigits[ #-1 ]&, 100 ]
%o A007954 (PARI) A007954(n)= { local(resul); if(n<10, return(n) ); resul = n % 
               10; n = (n - n%10)/10; while( n > 0, resul *= n %10; n = (n - n%10)/
               10; ); return(resul); } { for(n=0,50, print1(A007954(n),","); ); 
               } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 23 2006
%Y A007954 Cf. A031347 (different from A035930), A007953, A010888.
%Y A007954 Cf. A093811, A008683, A000012. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Mar 22 2009]
%Y A007954 Sequence in context: A031347 A087471 A128212 this_sequence A079475 A081286 
               A080867
%Y A007954 Adjacent sequences: A007951 A007952 A007953 this_sequence A007955 A007956 
               A007957
%K A007954 nonn,base,easy,nice
%O A007954 0,3
%A A007954 R. Muller
%E A007954 Error in term 25 corrected 11/95.