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A163100 Triangle giving positive values of A147861.

%I A163100 #7 Mar 04 2019 01:26:30
%S A163100 1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,2,2,1,1,3,1,1,2,2,1,1,1,1,2,3,3,2,
%T A163100 1,1,1,1,2,2,1,1,3,3,1,1,2,4,2,1,1,1,1,2,3,3,2,1,1,1,1,2,4,4,2,1,1,3,
%U A163100 3,1,1,2,2,1,1,1,1,2,3,4,4,3,2,1,1,5,1,1,2,2,1,1,3,3,1,1,2,4,4,2,1,1,1,1,2
%N A163100 Triangle giving positive values of A147861.
%H A163100 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>
%H A163100 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polprdipi.jpg">Illustration: Divisors and pi(x)</a>
%e A163100 Triangle begins:
%e A163100 1;
%e A163100 1,1;
%e A163100 1,..1;
%e A163100 1,2,..1;
%e A163100 1,......1;
%e A163100 1,2,2,....1;
%e A163100 1,..........1;
%e A163100 1,2,..2,......1;
%e A163100 1,..3,..........1;
%e A163100 1,2,....2,........1;
%e A163100 1,..................1;
%e A163100 1,2,3,3,..2,..........1;
%e A163100 1,......................1;
%e A163100 1,2,........2,............1;
%e A163100 1,..3,..3,..................1;
%e A163100 1,2,..4,......2,..............1;
%e A163100 1,..............................1;
%e A163100 1,2,3,....3,....2,................1;
%e A163100 1,..................................1;
%e A163100 1,2,..4,4,........2,..................1;
%e A163100 1,..3,......3,..........................1;
%e A163100 1,2,................2,....................1;
%e A163100 1,..........................................1;
%e A163100 1,2,3,4,..4,..3,......2,......................1;
%e A163100 1,......5,......................................1;
%e A163100 1,2,....................2,........................1;
%e A163100 1,..3,..........3,..................................1;
%e A163100 1,2,..4,....4,............2,..........................1;
%e A163100 1,......................................................1;
%e A163100 1,2,3,..5,5,......3,........2,............................1;
%e A163100 ...
%e A163100 Row sums: A117004.
%p A163100 A147861 := proc(n,k) if k<=0 or k > n then 0; else if n mod k = 0 then min(k,n/k) ; else 0; fi; fi; end proc: A163100 := proc(n,k) local dvs; dvs := sort(convert(numtheory[divisors](n),list)) ; min( op(k,dvs),n/op(k,dvs)) ; end: for n from 1 to 60 do for k from 1 to numtheory[tau](n) do printf("%d,",A163100(n,k) ) ; end do; end do: # _R. J. Mathar_, Aug 01 2009
%Y A163100 Cf. A000005, A008578, A027750, A051731, A117004, A127093, A147861, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.
%K A163100 easy,nonn,tabf
%O A163100 1,7
%A A163100 _Omar E. Pol_, Jul 20 2009
%E A163100 Extended beyond row 12 by _R. J. Mathar_, Aug 01 2009