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%I #37 Mar 30 2024 11:36:01
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,29,30,31,34,
%T 37,39,40,41,43,46,49,50,51,59,60,61,64,67,69,70,71,73,76,79,80,81,89,
%U 90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112
%N Numbers whose decimal representation contains the digital root of the product of their digits.
%C All numbers with a 0 digit (A011540) are terms, since their product of digits is 0.
%C All numbers with a 9 digit (A011539) are terms, since their product of digits is a multiple of 9 and so has digital root 9 if no 0 digits, or 0 if any 0 digit.
%e 29 is a term because 2*9=18 and 1+8=9 and 29 contains digit 9.
%t digRoot[n_] := If[n == 0, 0, Mod[n - 1, 9] + 1]; q[n_] := Module[{d = IntegerDigits[n]}, MemberQ[d, digRoot[Times @@ d]]]; Select[Range[0, 112], q] (* _Amiram Eldar_, Mar 11 2024 *)
%Y Cf. A007954, A010888, A011539, A011540, A119246.
%K nonn,base,easy
%O 1,3
%A _Saish S. Kambali_, Mar 11 2024