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