A319068 - OEIS

%I #9 Jun 14 2020 09:40:45

%S 1,1,2,3,1,5,4,7,2,1,1,11,9,13,8,7,1,17,1,19,4,1,1,23,1,9,2,13,1,29,

%T 25,31,2,1,4,22,1,37,18,27,1,41,1,43,8,1,1,47,4,1,2,9,1,53,1,39,49,1,

%U 1,59,1,61,32,31,9,5,1,67,2,13,1,71,1,73,8,37,4,45,1,79

%N a(n) is the greatest k such that A000203(k) divides n where A000203 is the sum of divisors of n.

%C Sándor names this function the sum-of-divisors maximum function and remarks that this function is well-defined, since a(n) can be at least 1, and cannot be greater than n.

%H Antti Karttunen, <a href="/A319068/b319068.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A319068/a319068.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H József Sándor, <a href="https://rgmia.org/papers/v8n1/art4.pdf">The sum-of-divisors minimum and maximum functions</a>, Research Report Collection, Volume 8, Issue 1, 2005. See pp. 3-4.

%F a(p+1) = p, for p prime. See Sándor Theorem 2 p. 4.

%o (PARI) a(n) = {forstep (k=n, 1, -1, if ((n % sigma(k)) == 0, return (k)););}

%Y Cf. A000203 (sigma), A070982 (the sum of divisors minimum function).

%K nonn

%O 1,3

%A _Michel Marcus_, Sep 09 2018