cp's OEIS Frontend

A057144 Smallest of the most frequently occurring numbers in 1-to-n multiplication table.

%I A057144 #18 Mar 29 2022 15:10:39
%S A057144 1,2,2,4,4,6,6,6,6,6,6,12,12,12,12,12,12,36,36,60,60,60,60,24,24,24,
%T A057144 24,24,24,60,60,60,60,60,60,60,60,60,60,120,120,120,120,120,120,120,
%U A057144 120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120
%N A057144 Smallest of the most frequently occurring numbers in 1-to-n multiplication table.
%H A057144 Branden Aldridge, <a href="/A057144/b057144.txt">Table of n, a(n) for n = 1..20000</a> (terms 1..1000 from Reinhard Zumkeller, terms 1001..10000 from Reinhard Zumkeller and Charles R Greathouse IV)
%H A057144 Benjamin Dickman, <a href="https://math.stackexchange.com/questions/776447/what-number-appears-most-often-in-an-n-times-n-multiplication-table">What number appears most often in an n X n multiplication table?</a>, Mathematics StackExchange, May 2014.
%e A057144 M(n) is the array in which m(x,y)= x*y for x = 1 to n and y = 1 to n. In m(10), the most frequently occurring numbers are 6, 8, 10, 12, 18, 20, 24, 30,40, each occurring 4 times. The smallest of these numbers is 6, so a(10) = 6.
%o A057144 (Haskell)
%o A057144 import Data.List (sort, group, sortBy, groupBy)
%o A057144 import Data.Function (on)
%o A057144 a057144 n = head $ last $ head $ groupBy ((==) `on` length) $
%o A057144             reverse $ sortBy (compare `on` length) $
%o A057144             group $ sort [u * v | u <- [1..n], v <- [1..n]]
%o A057144 -- _Reinhard Zumkeller_, Jun 22 2013
%o A057144 (PARI) T(n,f=factor(n))=my(k=#f~); f[,1]=primes(k+1)[2..k+1]~; f[1,1]=6; factorback(f)
%o A057144 listA025487(Nmax)=vecsort(concat(vector(logint(Nmax, 2), n, select(t->t<=Nmax, if(n>1, [factorback(primes(#p), Vecrev(p))|p<-partitions(n)], [1, 2])))))
%o A057144 ct(n,k)=sumdiv(n,d,max(d,n/d)<=k)
%o A057144 a(n)=if(n==1, return(1)); my(v=listA025487(n^2),r,t,at); for(i=1,#v, t=ct(v[i],n); if(t>r, r=t; at=v[i])); at \\ _Charles R Greathouse IV_, Feb 05 2022
%Y A057144 Cf. A057142, A057143, A057338.
%K A057144 nonn
%O A057144 1,2
%A A057144 _Arran Fernandez_, Aug 13 2000
%E A057144 More terms from Larry Reeves (larryr(AT)acm.org), Apr 18 2001