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

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, 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, 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

Offset: 1

Author

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

Keywords

• nonn

Examples

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

Links

• Branden Aldridge, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A064047, A057142, A057143, A057144.

Programs

Mathematica

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 *)

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(tr,ct=1;r=t, ct++)); ct \\ Charles R Greathouse IV, Feb 05 2022