A265719 Numbers n such that Sum_{d|n} 1/tau(d) > Sum_{d|m} 1/tau(d) for all m < n.
1, 2, 4, 6, 12, 24, 30, 48, 60, 120, 180, 210, 240, 360, 420, 720, 840, 1260, 1680, 2520, 4620, 5040, 7560, 9240, 13860, 18480, 27720, 55440, 83160, 110880, 120120, 166320, 180180, 240240, 360360, 720720, 1081080, 1441440, 1801800, 2042040, 2162160, 3063060, 3603600, 4084080
Offset: 1
Keywords
Examples
For n = 4; a(4) = 6 because 6 is the smallest number such that Sum_{d|a(4)} 1/tau(d) = Sum_{d|6} 1/tau(d) = 9/4 > Sum_{d|a(3)} 1/tau(d) = Sum_{d|4} 1/tau(d) = 11/6.
Programs
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Magma
a:=1; S:=[a]; for n in [2..25] do k:=0; flag:= true; while flag do k+:=1; if &+[1/NumberOfDivisors(d): d in Divisors(a)] lt &+[1/NumberOfDivisors(d): d in Divisors(k)] then Append(~S, k); a:=k; flag:=false; end if; end while; end for; S;
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PARI
lista(nn) = {m = 0; for (n=1, nn, if ((mm = sumdiv(n, d, 1/numdiv(d))) > m, print1(n, ", "); m = mm););} \\ Michel Marcus, Dec 22 2015
Extensions
More terms from Michel Marcus, Dec 22 2015
Comments