A371123 Numbers whose decimal representation contains the digital root of the product of their digits.

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

Author

Saish S. Kambali, Mar 11 2024

Keywords

• nonn
• base
• easy

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.

Examples

			29 is a term because 2*9=18 and 1+8=9 and 29 contains digit 9.
		

Crossrefs

Cf. A007954, A010888, A011539, A011540, A119246.

Programs

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 *)