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

1, 2, 4, 6, 12, 12, 36, 60, 60, 60, 120, 120, 120, 120, 360, 360, 360, 360, 360, 360, 840, 840, 840, 840, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 2520, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 10080, 10080

Offset: 1

Author

Ron Lalonde (ronronronlalonde(AT)hotmail.com), Jun 25 2001

Keywords

• nonn

Comments

Smallest number to appear n times in any m X m multiplication table.

Examples

			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.
		

Crossrefs

Cf. A027424, A062851, A062854, A062855, A062857, A062858, A062859.

Programs

Mathematica

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]]}] ]];
a[n_] := b[n][[2]];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Mar 25 2019 *)

Python

from itertools import count
from collections import Counter
def A062856(n):
    if n == 1: return 1
    c = Counter()
    for m in count(1):
        for i in range(1,m):
            ij = i*m
            c[ij] += 2
            if c[ij]>=n:
                return ij
        c[m*m] = 1 # Chai Wah Wu, Oct 16 2023

Extensions

More terms from Don Reble, Nov 08 2001