A163100 Triangle giving positive values of A147861.

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, 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, 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

Offset: 1

Author

Omar E. Pol, Jul 20 2009

Keywords

• easy
• nonn
• tabf

Examples

			Triangle begins:
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,..........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,......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;
1,2,3,..5,5,......3,........2,............................1;
...
Row sums: A117004.
		

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
• Omar E. Pol, Illustration: Divisors and pi(x)

Crossrefs

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

Programs

Maple

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

Extensions

Extended beyond row 12 by R. J. Mathar, Aug 01 2009