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Triangle giving positive values of A147861.
8

%I #7 Mar 04 2019 01:26:30

%S 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 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 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 Triangle giving positive values of A147861.

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polprdipi.jpg">Illustration: Divisors and pi(x)</a>

%e Triangle begins:

%e 1;

%e 1,1;

%e 1,..1;

%e 1,2,..1;

%e 1,......1;

%e 1,2,2,....1;

%e 1,..........1;

%e 1,2,..2,......1;

%e 1,..3,..........1;

%e 1,2,....2,........1;

%e 1,..................1;

%e 1,2,3,3,..2,..........1;

%e 1,......................1;

%e 1,2,........2,............1;

%e 1,..3,..3,..................1;

%e 1,2,..4,......2,..............1;

%e 1,..............................1;

%e 1,2,3,....3,....2,................1;

%e 1,..................................1;

%e 1,2,..4,4,........2,..................1;

%e 1,..3,......3,..........................1;

%e 1,2,................2,....................1;

%e 1,..........................................1;

%e 1,2,3,4,..4,..3,......2,......................1;

%e 1,......5,......................................1;

%e 1,2,....................2,........................1;

%e 1,..3,..........3,..................................1;

%e 1,2,..4,....4,............2,..........................1;

%e 1,......................................................1;

%e 1,2,3,..5,5,......3,........2,............................1;

%e ...

%e Row sums: A117004.

%p 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 Cf. A000005, A008578, A027750, A051731, A117004, A127093, A147861, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.

%K easy,nonn,tabf

%O 1,7

%A _Omar E. Pol_, Jul 20 2009

%E Extended beyond row 12 by _R. J. Mathar_, Aug 01 2009