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Smallest nontrivial multiple of n whose nonzero digit product is the same as that of the nonzero digit product of n. By nontrivial one means a(n) is not equal to n or (10^k)*n. 0 if no such number exists.
2

%I #12 Aug 12 2017 02:25:33

%S 11,12,1113,104,15,132,1071,24,11133,110,1001,1020,1131,1022,105,32,

%T 1071,108,133,120,100002,1122,161,1008,125,1430,702,224,3016,11130,

%U 10013,160,3003,612,315,1332,703,342,11193,1040,10004,1008,602,1144,225

%N Smallest nontrivial multiple of n whose nonzero digit product is the same as that of the nonzero digit product of n. By nontrivial one means a(n) is not equal to n or (10^k)*n. 0 if no such number exists.

%C Conjecture: no term is zero.

%H Chai Wah Wu, <a href="/A087304/b087304.txt">Table of n, a(n) for n = 1..10000</a>

%F a(10*n) = a(n)*10. - _Chai Wah Wu_, Aug 11 2017

%e a(19) = 133 = 19*7 and 1*3*3 = 1*9.

%o (Python)

%o from functools import reduce

%o from operator import mul

%o def A087304(n):

%o i, p = 2, reduce(mul,(int(d) for d in str(n) if d != '0'))

%o while (max(str(i)) == '1' and str(i).count('1') == 1) or reduce(mul,(int(d) for d in str(i*n) if d != '0')) != p:

%o i += 1

%o return i*n # _Chai Wah Wu_, Aug 11 2017

%o (PARI) prd(n) = {my(d = digits(n), p = 1); for (k=1, #d, if (d[k], p *= d[k]);); p;}

%o a(n) = {my(k = 2, prdn = prd(n)); while (prd(k*n) != prdn, k++; if (! (k % 10), k++)); k*n;} \\ _Michel Marcus_, Aug 12 2017

%Y Cf. A051801.

%K base,look,nonn

%O 1,1

%A _Amarnath Murthy_, Sep 01 2003

%E More terms from _David Wasserman_, Apr 19 2005