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A057144 Smallest of the most frequently occurring numbers in 1-to-n multiplication table. 10
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, 24, 24, 24, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120 (list; graph; refs; listen; history; text; internal format)
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)
Benjamin Dickman, What number appears most often in an n X n multiplication table?, Mathematics StackExchange, May 2014.
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(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.
PROG
(Haskell)
import Data.List (sort, group, sortBy, groupBy)
import Data.Function (on)
a057144 n = head $ last $ head $ groupBy ((==) `on` length) $
reverse $ sortBy (compare `on` 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, 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
CROSSREFS
Sequence in context: A007730 A330271 A257686 * A198332 A080606 A083535
KEYWORD
nonn
AUTHOR
Arran Fernandez, Aug 13 2000
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Apr 18 2001
STATUS
approved

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Last modified March 1 06:29 EST 2024. Contains 370430 sequences. (Running on oeis4.)