A114104 - OEIS

%I #11 May 23 2024 04:41:19

%S 1,1,2,3,3,1,4,1,4,2,5,5,5,5,1,3,6,1,6,3,2,7,7,7,7,7,7,1,8,4,8,1,8,4,

%T 8,2,9,9,3,9,9,3,9,9,1,5,10,5,10,1,10,5,10,5,2,11,11,11,11,11,11,11,

%U 11,11,11,1,12,3,4,6,12,1,12,6,4,3,12,2,13,13

%N a(n) = A114103(n)/n.

%C Iff k appears k-1 times successively then k is prime.

%p A000217 := proc(n) n*(n+1)/2 ; end: A003056 := proc(n) floor((sqrt(1+8*n)-1)/2) ; end: A114103 := proc(n,k) lcm(n,A000217(n-1)+k) ; end: A114104 := proc(n) local row,col ; row := A003056(n-1)+1 ; col := n-A000217(row-1) ; A114103(row,col)/n ; end: for n from 1 to 80 do printf("%d, ",A114104(n)) ; od ; # _R. J. Mathar_, May 10 2007

%t rows = 13;

%t nmax = rows (rows + 1)/2;

%t A114103 = Flatten[Table[LCM[n, n (n-1)/2 + k], {n, rows}, {k, n}]];

%t a[n_] := A114103[[n]]/n;

%t Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, May 23 2024, after _Ivan Neretin_ in A114103 *)

%Y Cf. A114103, A114105.

%K nonn

%O 1,3

%A _Amarnath Murthy_, Nov 21 2005

%E Corrected and extended by _R. J. Mathar_, May 10 2007