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

1,2

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).

Example

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.

Prog

(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

Crossrefs

Cf. A057143, A057144, A057338.

Sequence in context: A340611 A068509 A070319 * A320837 A098388 A371672

Adjacent sequences: A057139 A057140 A057141 * A057143 A057144 A057145

Keyword

nonn

Author

Arran Fernandez, Aug 13 2000

Extensions

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

Status

approved