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A069518 Geometric mean of digits = 4 and digits are in nondecreasing order.

%I A069518 #12 Apr 29 2021 00:57:08
%S A069518 4,28,44,188,248,444,1488,2288,2448,4444,12888,14488,22488,24448,
%T A069518 44444,118888,124888,144488,222888,224488,244448,444444,1148888,
%U A069518 1228888,1244888,1444488,2224888,2244488,2444448,4444444,11288888,11448888,12248888,12444888
%N A069518 Geometric mean of digits = 4 and digits are in nondecreasing order.
%C A069518 No number is obtainable by permuting the digits of other members - only one with ascending order of digits is included.
%H A069518 Michael S. Branicky, <a href="/A069518/b069518.txt">Table of n, a(n) for n = 1..10000</a>
%e A069518 1488 is a term but 1848 is not.
%t A069518 a = {}; b = 4; 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, 10^7}]
%o A069518 (Python)
%o A069518 from math import prod
%o A069518 from sympy.utilities.iterables import multiset_combinations
%o A069518 def auptod(terms):
%o A069518   n, digits, alst, powsexps2 = 0, 1, [], [(1, 0), (2, 1), (4, 2), (8, 3)]
%o A069518   while n < terms:
%o A069518     target = 4**digits
%o A069518     mcstr = "".join(str(d)*(digits//max(1, r//2)) for d, r in powsexps2)
%o A069518     for mc in multiset_combinations(mcstr, digits):
%o A069518       if prod(map(int, mc)) == target:
%o A069518         n += 1
%o A069518         alst.append(int("".join(mc)))
%o A069518         if n == terms: break
%o A069518     else: digits += 1
%o A069518   return alst
%o A069518 print(auptod(34)) # _Michael S. Branicky_, Apr 28 2021
%Y A069518 Cf. A061428, A069512, A069516.
%K A069518 nonn,base
%O A069518 1,1
%A A069518 _Amarnath Murthy_, Mar 30 2002
%E A069518 Edited and extended by _Robert G. Wilson v_, Apr 01 2002
%E A069518 Name edited and a(31) and beyond from _Michael S. Branicky_, Apr 28 2021