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

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, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Arran Fernandez, Aug 13 2000

Keywords

• nonn

Examples

			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.
		

Links

• Branden Aldridge, Table of n, a(n) for n = 1..20000 (terms 1..1000 from Reinhard Zumkeller, terms 1001..10000 from Reinhard Zumkeller and Charles R Greathouse IV).

Crossrefs

Cf. A057143, A057144, A057338.

Programs

Haskell

import Data.List (group, sort)
a057142 n = head $ reverse $ sort $ map length $ group $
            sort [u * v | u <- [1..n], v <- [1..n]]
-- Reinhard Zumkeller, Jun 22 2013

PARI

T(n,f=factor(n))=my(k=#f~); f[,1]=primes(k+1)[2..k+1]~; f[1,1]=6; factorback(f)
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])))))
ct(n,k)=sumdiv(n,d,max(d,n/d)<=k)
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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 18 2001