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A069516 Geometric mean of digits = 3 and digits are in nondecreasing order.

%I A069516 #12 Apr 29 2021 00:57:22
%S A069516 3,19,33,139,333,1199,1339,3333,11399,13339,33333,111999,113399,
%T A069516 133339,333333,1113999,1133399,1333339,3333333,11119999,11133999,
%U A069516 11333399,13333339,33333333,111139999,111333999,113333399,133333339,333333333,1111199999,1111339999
%N A069516 Geometric mean of digits = 3 and digits are in nondecreasing order.
%C A069516 No number is obtainable by permuting the digits of other members - only one with ascending order of digits is included.
%H A069516 Michael S. Branicky, <a href="/A069516/b069516.txt">Table of n, a(n) for n = 1..10000</a>
%e A069516 1339 belongs to this sequence but 1933 does not.
%t A069516 a = {}; b = 3; Do[c = Apply[ Times, IntegerDigits[n]]/b^Floor[ Log[10, n] + 1]; If[c == 1 && Position[a, FromDigits[ Sort[ IntegerDigits[n]]]] == {}, Print[n]; a = Append[a, n]], {n, 1, 10^8}]
%o A069516 (Python)
%o A069516 from math import prod
%o A069516 from sympy.utilities.iterables import multiset_combinations
%o A069516 def aupton(terms):
%o A069516   n, digits, alst, powsexps3 = 0, 1, [], [(1, 0), (3, 1), (9, 2)]
%o A069516   while n < terms:
%o A069516     target = 3**digits
%o A069516     mcstr = "".join(str(d)*(digits//max(1, r)) for d, r in powsexps3)
%o A069516     for mc in multiset_combinations(mcstr, digits):
%o A069516       if prod(map(int, mc)) == target:
%o A069516         n += 1
%o A069516         alst.append(int("".join(mc)))
%o A069516         if n == terms: break
%o A069516     else: digits += 1
%o A069516   return alst
%o A069516 print(aupton(31)) # _Michael S. Branicky_, Apr 28 2021
%Y A069516 Cf. A061427, A069512, A069518.
%K A069516 nonn,base
%O A069516 1,1
%A A069516 _Amarnath Murthy_, Mar 30 2002
%E A069516 Edited and extended by _Robert G. Wilson v_, Apr 01 2002
%E A069516 Name edited and a(30) and beyond from _Michael S. Branicky_, Apr 28 2021