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A371123
Numbers whose decimal representation contains the digital root of the product of their digits.
0
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, 37, 39, 40, 41, 43, 46, 49, 50, 51, 59, 60, 61, 64, 67, 69, 70, 71, 73, 76, 79, 80, 81, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112
OFFSET
1,3
COMMENTS
All numbers with a 0 digit (A011540) are terms, since their product of digits is 0.
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.
EXAMPLE
29 is a term because 2*9=18 and 1+8=9 and 29 contains digit 9.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Saish S. Kambali, Mar 11 2024
STATUS
approved