A070324 a(n) = Max( sigma(k) : k=1,2,3,...,n ).

1, 3, 4, 7, 7, 12, 12, 15, 15, 18, 18, 28, 28, 28, 28, 31, 31, 39, 39, 42, 42, 42, 42, 60, 60, 60, 60, 60, 60, 72, 72, 72, 72, 72, 72, 91, 91, 91, 91, 91, 91, 96, 96, 96, 96, 96, 96, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 168, 168, 168, 168, 168, 168

Offset: 1

Author

Benoit Cloitre, May 11 2002

Keywords

• easy
• nonn

Comments

Records give A034885. Where records occur gives A002093. - Omar E. Pol, Apr 23 2020

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000
• Amiram Eldar, Plot of (1/n^2) * Sum_{i=1..n} a(i) for n = 2^(1..33).

Crossrefs

Cf. A000203, A002093, A034885.

Programs

Mathematica

FoldList[Max, DivisorSigma[1, Range[100]]] (* Amiram Eldar, Dec 27 2024 *)

PARI

a(n)=vecmax(vector(n,k, sigma(k)))

Formula

Limit_{n -> infinity} (1/n^2) * Sum_{i=1..n} a(i) = C = 1.2... . [This formula is wrong. See the graph. - Amiram Eldar, Dec 27 2024]