A266228 Numbers n such that Sum_{d|n} 1/sigma(d) > Sum_{d|m} 1/sigma(d) for all m < n.

1, 2, 4, 6, 12, 24, 30, 36, 48, 60, 120, 180, 240, 360, 420, 720, 840, 1260, 1680, 2520, 5040, 10080, 13860, 15120, 18480, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 360360, 720720, 1441440, 2162160, 3603600, 4324320, 6126120, 7207200, 10810800, 12252240, 21621600, 24504480, 36756720, 61261200, 73513440

Offset

1,2

Comments

Where record values of Sum_{d|n} 1/sigma(d) occur.

Links

Table of n, a(n) for n=1..47.

Example

For n = 4; a(4) = 6 because 6 is the smallest number such that Sum_{d|a(4)} 1/sigma(d) = Sum_{d|6} 1/sigma(d) = 5/3 > Sum_{d|a(3)} 1/sigma(d) = Sum_{d|4} 1/sigma(d) = 31/21.

Prog

(Magma) a:=1; S:=[a]; for n in [2..25] do k:=0; flag:= true; while flag do k+:=1; if &+[1/SumOfDivisors(d): d in Divisors(a)] lt &+[1/SumOfDivisors(d): d in Divisors(k)] then Append(~S, k); a:=k; flag:=false; end if; end while; end for; S;
(PARI) b(n)={sumdiv(n, d, 1/sigma(d)); }
{ my(m=0); for(n=1, 1e6, if(b(n)>m, m=b(n); print1(n, ", "))) } \\ Andrew Howroyd, Nov 11 2018

Crossrefs

Cf. A069934, A000203, A265708, A265709, A265710, A265711, A265712, A265713, A265714, A266227.

Sequence in context: A129301 A066523 A097212 * A362081 A265719 A126098

Adjacent sequences: A266225 A266226 A266227 * A266229 A266230 A266231

Keyword

nonn

Author

Jaroslav Krizek, Dec 24 2015

Extensions

a(35)-a(47) from Andrew Howroyd, Nov 11 2018

Status

approved