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Numbers n for which the digital product A007954(n) contains the same distinct digits as the number n.
3

%I #16 Sep 08 2022 08:46:10

%S 0,1,2,3,4,5,6,7,8,9,11,111,1111,1288,1557,1575,1755,1828,1882,2188,

%T 2818,2881,3448,3484,3577,3757,3775,3844,4348,4384,4438,4483,4834,

%U 4843,5157,5175,5377,5517,5571,5715,5737,5751,5773,7155,7357,7375,7515,7537,7551

%N Numbers n for which the digital product A007954(n) contains the same distinct digits as the number n.

%H Harvey P. Dale, <a href="/A249516/b249516.txt">Table of n, a(n) for n = 1..1000</a>

%e 1288 is a member since 1288 and its digital product 1*2*8*8 = 128 have the same digit set {1,2,8}.

%t Select[Range[0,8000],Union[IntegerDigits[Times@@IntegerDigits[#]]] == Union[ IntegerDigits[#]]&] (* _Harvey P. Dale_, Aug 05 2018 *)

%o (Magma) [n: n in [0..100000] | Set(Intseq(n)) eq Set(Intseq(&*Intseq(n)))]

%o (PARI) print1(0,", ");for(n=1,10^4,d=digits(n);p=prod(i=1,#d,d[i]);if(vecsort(digits(p),,8)==vecsort(d,,8),print1(n,", "))) \\ _Derek Orr_, Nov 05 2014

%Y Cf. A007954, A249515, A249517.

%K nonn,base,easy

%O 1,3

%A _Jaroslav Krizek_, Oct 31 2014