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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 Cf. A057142, A057143, A057338. Sequence in context: A007730 A330271 A257686 * A198332 A080606 A083535 Adjacent sequences: A057141 A057142 A057143 * A057145 A057146 A057147 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.)