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A057144
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Smallest of the most frequently occurring numbers in 1-to-n multiplication table.
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10
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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PROG
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(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]]
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 18 2001
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STATUS
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approved
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