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A057142 Occurrences of most frequently occurring number in 1-to-n multiplication table.

%I A057142 #17 Mar 29 2022 12:26:24
%S A057142 1,2,2,3,3,4,4,4,4,4,4,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,10,10,10,
%T A057142 10,10,10,10,10,10,10,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,
%U A057142 12,12,12,12,14,14,14,14,14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16
%N A057142 Occurrences of most frequently occurring number in 1-to-n multiplication table.
%H A057142 Branden Aldridge, <a href="/A057142/b057142.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).
%e A057142 M(n) is the array in which m(x,y)= x*y for x = 1 to n and y = 1 to n. In m(5), the most frequently occurring number is 4. It occurs 3 times, so a(5) = 3.
%o A057142 (Haskell)
%o A057142 import Data.List (group, sort)
%o A057142 a057142 n = head $ reverse $ sort $ map length $ group $
%o A057142             sort [u * v | u <- [1..n], v <- [1..n]]
%o A057142 -- _Reinhard Zumkeller_, Jun 22 2013
%o A057142 (PARI) T(n,f=factor(n))=my(k=#f~); f[,1]=primes(k+1)[2..k+1]~; f[1,1]=6; factorback(f)
%o A057142 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 A057142 ct(n,k)=sumdiv(n,d,max(d,n/d)<=k)
%o A057142 a(n)=if(n==1, return(1)); my(v=listA025487(n^2),r,t); for(i=1,#v, t=ct(v[i],n); if(t>r, r=t)); r \\ _Charles R Greathouse IV_, Feb 05 2022
%Y A057142 Cf. A057143, A057144, A057338.
%K A057142 nonn
%O A057142 1,2
%A A057142 _Arran Fernandez_, Aug 13 2000
%E A057142 More terms from Larry Reeves (larryr(AT)acm.org), Apr 18 2001