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A062856 In the square multiplication table of size A062857(n), the smallest number which appears n times.

%I A062856 #12 Oct 16 2023 23:29:38
%S A062856 1,2,4,6,12,12,36,60,60,60,120,120,120,120,360,360,360,360,360,360,
%T A062856 840,840,840,840,2520,2520,2520,2520,2520,2520,2520,2520,2520,2520,
%U A062856 5040,5040,5040,5040,5040,5040,5040,5040,5040,5040,5040,5040,10080,10080
%N A062856 In the square multiplication table of size A062857(n), the smallest number which appears n times.
%C A062856 Smallest number to appear n times in any m X m multiplication table.
%e A062856 a(7)=36 because 36 is the first product to appear in the m X m multiplication tables 7 times as m increases from 1 to infinity.
%t A062856 b[1] = {1, 1}; b[n_] := b[n] = For[m = b[n-1][[1]], True, m++, T = Table[i j, {i, m}, {j, m}] // Flatten // Tally; sel = SelectFirst[T, #[[2]] >= n&]; If[sel != {}, Print[n, " ", m, " ", sel[[1]]]; Return[{m, sel[[1]]}] ]];
%t A062856 a[n_] := b[n][[2]];
%t A062856 Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Mar 25 2019 *)
%o A062856 (Python)
%o A062856 from itertools import count
%o A062856 from collections import Counter
%o A062856 def A062856(n):
%o A062856     if n == 1: return 1
%o A062856     c = Counter()
%o A062856     for m in count(1):
%o A062856         for i in range(1,m):
%o A062856             ij = i*m
%o A062856             c[ij] += 2
%o A062856             if c[ij]>=n:
%o A062856                 return ij
%o A062856         c[m*m] = 1 # _Chai Wah Wu_, Oct 16 2023
%Y A062856 Cf. A027424, A062851, A062854, A062855, A062857, A062858, A062859.
%K A062856 nonn
%O A062856 1,2
%A A062856 Ron Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001
%E A062856 More terms from _Don Reble_, Nov 08 2001