A070324 - OEIS

%I #24 Dec 27 2024 04:39:18

%S 1,3,4,7,7,12,12,15,15,18,18,28,28,28,28,31,31,39,39,42,42,42,42,60,

%T 60,60,60,60,60,72,72,72,72,72,72,91,91,91,91,91,91,96,96,96,96,96,96,

%U 124,124,124,124,124,124,124,124,124,124,124,124,168,168,168,168,168,168

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

%C Records give A034885. Where records occur gives A002093. - _Omar E. Pol_, Apr 23 2020

%H Hugo Pfoertner, <a href="/A070324/b070324.txt">Table of n, a(n) for n = 1..10000</a>

%H Amiram Eldar, <a href="/A070324/a070324.jpg">Plot of (1/n^2) * Sum_{i=1..n} a(i) for n = 2^(1..33)</a>.

%F 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]

%t FoldList[Max, DivisorSigma[1, Range[100]]] (* _Amiram Eldar_, Dec 27 2024 *)

%o (PARI) a(n)=vecmax(vector(n,k, sigma(k)))

%Y Cf. A000203, A002093, A034885.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 11 2002