A061556 - OEIS

%I #40 Nov 21 2019 04:06:12

%S 1,1,3,5,9,14,23,43,79,149,263,461,823,1451,2549,4483,7879,13859,

%T 24247,42683,75037,131707,230773,405401,710569,1246379,2185021,

%U 3831913,6720059,11781551,20657677

%N a(n) is the least k > 0 such that sigma(k!) >= n*k!.

%C It seems that, for n > 1, a(n+1) < 2*a(n). Does lim_{n -> infinity} a(n+1)/a(n) = 2? - _Benoit Cloitre_, Aug 18 2002

%C Smallest number m such that the abundancy-index of m! is at least n.

%C Floor(sigma(m!)/m!) = n; note that abundancy-index [= sigma(u)/u] here is not necessarily an integer.

%C It appears that a(n) = A091440(n) for n >= 13. - _Daniel Suteu_, Sep 03 2019

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>.

%H Fred Helenius, <a href="https://web.archive.org/web/20171112075301/http://pw1.netcom.com/~fredh/index.html">Multiperfect numbers</a>.

%F a(n) = Min{w | floor(sigma(w!)/w!) = n}.

%e floor(sigma(842!)/842!) = 11 while floor(sigma(843!)/843!) = 12.

%o (PARI) a(n)=if(n<0,0,s=1; while(sigma(s!)<n*s!,s++); s)

%Y Cf. A000142, A000203, A023199, A062569.

%K nonn,more

%O 0,3

%A _Labos Elemer_, May 17 2001

%E More terms from _David Wasserman_, Jun 18 2002

%E a(1) inserted and a(21)-a(30) added by _Daniel Suteu_, Sep 03 2019