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A064048 Number of most frequently occurring numbers in the 1-to-n multiplication table. 2

%I #9 Mar 29 2022 15:10:29

%S 1,1,3,1,1,2,2,4,5,9,9,2,2,2,4,5,5,1,1,1,1,1,1,5,5,5,5,7,7,2,2,2,2,2,

%T 2,4,4,4,4,1,1,1,1,1,3,3,3,4,4,4,4,4,4,4,4,6,6,6,6,4,4,4,4,4,4,4,4,4,

%U 4,6,6,1,1,1,1,1,1,1,1,3,3,3,3,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2

%N Number of most frequently occurring numbers in the 1-to-n multiplication table.

%H Branden Aldridge, <a href="/A064048/b064048.txt">Table of n, a(n) for n = 1..20000</a>

%e In the 1-to-6 multiplication table, the most frequently occurring numbers (each occurring 4 times) are 6 and 12. Therefore a(6)=2.

%t mfon[n_]:=Module[{x=SortBy[Tally[Times@@@Tuples[Range[n],2]], Last]}, Length[ Select[x,#[[2]]==x[[-1,2]]&]]]; Array[mfon,100] (* _Harvey P. Dale_, Oct 20 2012 *)

%o (PARI) a(n)=my(v=List(),ct,s,r,t); for(a=1,n,for(b=1,n,listput(v,a*b))); s=Set(v); for(i=1,#s, t=sum(j=1,#v,v[j]==s[i]); if(t<r, next); if(t>r,ct=1;r=t, ct++)); ct \\ _Charles R Greathouse IV_, Feb 05 2022

%Y Cf. A064047, A057142, A057143, A057144.

%K nonn

%O 1,3

%A Matthew Somerville (matthew.somerville(AT)trinity.oxford.ac.uk), Aug 24 2001

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Last modified March 3 04:18 EST 2024. Contains 370499 sequences. (Running on oeis4.)