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%I #16 Mar 08 2023 01:11:02
%S 37,38,39,73,83,93,99,146,164,247,274,299,339,348,368,384,386,393,416,
%T 427,438,449,461,472,483,494,614,638,641,679,683,697,699,724,742,769,
%U 796,834,836,843,863,929,933,944,967,969,976,992,996,1149,1156,1165,1179
%N Numbers that leave their digital root as the remainder when the product of their digits is divided by the sum of their digits.
%H Robert Israel, <a href="/A346383/b346383.txt">Table of n, a(n) for n = 1..10000</a>
%e 3*7 == 1 (mod 3+7), digital root of 37 is 1, so 37 is a term.
%p filter:= proc(n) local L; L:= convert(n,base,10); convert(L,`*`) mod convert(L,`+`) = [9,$1..8][(n mod 9)+1] end proc;
%t l={};Do[If[Mod[Times@@IntegerDigits@n,Total[IntegerDigits[n]]]==FixedPoint[Total[IntegerDigits[#, 10]] &, n],AppendTo[l,n]],{n,0,1000}];l
%o (PARI) isok(m) = my(d=digits(m)); (vecprod(d) % vecsum(d)) == ((m-1)%9 + 1); \\ _Michel Marcus_, Jul 15 2021
%Y Cf. A007953, A007954, A010888.
%K nonn,base
%O 1,1
%A _Metin Sariyar_, Jul 14 2021
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