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Smallest k such that sigma(k) >= n.
3

%I #22 Jul 25 2016 02:21:45

%S 1,2,2,3,4,4,4,6,6,6,6,6,8,8,8,10,10,10,12,12,12,12,12,12,12,12,12,12,

%T 16,16,16,18,18,18,18,18,18,18,18,20,20,20,24,24,24,24,24,24,24,24,24,

%U 24,24,24,24,24,24,24,24,24,30,30,30,30,30,30,30,30,30,30,30,30,36,36

%N Smallest k such that sigma(k) >= n.

%C Also smallest m to partition n into distinct divisors of m; highly abundant numbers are record values: a(i) < A002093(n) for 1<=i < A085443(n), A002093(n)=a(A085443(n)). - _Reinhard Zumkeller_, Jun 30 2003

%H Harvey P. Dale, <a href="/A070172/b070172.txt">Table of n, a(n) for n = 1..1000</a>

%F It seems that lim n -> infinity a(n)/n*log(log(n))=C=0.6...

%t nn=80;With[{s=Table[{n,DivisorSigma[1,n]},{n,nn}]},Transpose[ Flatten[ Table[ Select[s,#[[2]]>=i&,1],{i,nn}],1]][[1]]] (* _Harvey P. Dale_, Dec 28 2013 *)

%o (PARI) for(n=1,150,s=1; while(sigma(s)<n,s++); print1(s,","))

%Y Cf. A002093.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, May 06 2002