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a(n) = (A112565(n) - 1)/n for n>=1.
6

%I #9 Jun 23 2020 19:09:57

%S 1,3,9,31,109,421,1585,5454,20681,80983,311221,1168531,4505761,

%T 17907735,69240865,272109736,1078430833,4147985381,16383884581,

%U 64335012378,234179431201,929947274509,3651532869601,14453209093051,56596999501225

%N a(n) = (A112565(n) - 1)/n for n>=1.

%C A112565 is the main diagonal of square table A112564 of generalized Flavius Josephus sieves.

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%o (PARI) {a(n)=local(A=n,B=0,k=0);if(n<1,0, until(A==B,k=k+1;if(k%n==0,k=k+1);B=A;A=floor(A*(k+1)/k));A/n)}

%Y Cf. A112564, A112565, A112567.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 14 2005

%E More terms from _David Wasserman_, Jun 30 2009