A300826 - OEIS

%I #8 Mar 21 2018 17:18:46

%S 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,2,1,2,1,1,1,1,

%T 1,3,1,1,1,2,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,1,1,2,1,1,

%U 1,2,1,3,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,2,1,3,1,1,1,1,1,3,1,1,1,2,1,2,1,2,1

%N a(n) = n/A125746(n), where A125746(n) gives the smallest divisor d of n such that the sum which includes d and all smaller divisors is >= n.

%C Records occur at 1, 6, 24, 120, 240, 504, 1260, 2520, 5040, 15120, 50400, 55440, ... and they are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, ...

%H Antti Karttunen, <a href="/A300826/b300826.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = n/A125746(n).

%o (PARI) A300826(n) = { my(k=0,s=0); fordiv(n,d, k++; s += d; if(s>=n,return(n/d))); };

%Y Cf. A125746.

%Y Cf. A005100 (positions of ones), A023196 (positions of terms > 1).

%K nonn

%O 1,6

%A _Antti Karttunen_, Mar 21 2018