A073348 Least k such that sigma(k)/k >= sigma(n)/n.

1, 2, 2, 4, 2, 6, 2, 6, 2, 6, 2, 12, 2, 4, 4, 6, 2, 12, 2, 12, 4, 4, 2, 24, 2, 4, 2, 6, 2, 24, 2, 6, 2, 4, 2, 36, 2, 4, 2, 12, 2, 12, 2, 6, 4, 4, 2, 48, 2, 6, 2, 6, 2, 12, 2, 12, 2, 4, 2, 60, 2, 4, 4, 6, 2, 12, 2, 6, 2, 12, 2, 60, 2, 4, 4, 6, 2, 12, 2, 12, 2, 4, 2, 60, 2, 4, 2, 12, 2, 60, 2, 6, 2, 4

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

It seems that Sum_{k=1..n} a(k) is asymptotic to C*n*log(n)*log(log(n)) with C>1.

Mathematica

a[n_] := Module[{k = 1, r = DivisorSigma[-1, n]}, While[DivisorSigma[-1, k] < r, k++]; k]; Array[a, 100] (* Amiram Eldar, May 05 2022 *)

Prog

(PARI) a(n)=if(n<0, 0, s=1; while(sigma(s)/s<sigma(n)/n, s++); s)

Crossrefs

Cf. A000203, A017665, A017666.

Sequence in context: A074369 A323407 A354875 * A287093 A122457 A319410

Adjacent sequences: A073345 A073346 A073347 * A073349 A073350 A073351

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 23 2002

Status

approved