A162190 -id:A162190 - cp's OEIS frontend

A162348 List of pairs (i,j) of central factors of n, such that i*j = n, where i is the largest divisor of n <= sqrt(n) and j is the smallest divisor of n >= sqrt(n).

1, 1, 1, 2, 1, 3, 2, 2, 1, 5, 2, 3, 1, 7, 2, 4, 3, 3, 2, 5, 1, 11, 3, 4, 1, 13, 2, 7, 3, 5, 4, 4, 1, 17, 3, 6, 1, 19, 4, 5, 3, 7, 2, 11, 1, 23, 4, 6, 5, 5, 2, 13, 3, 9, 4, 7, 1, 29, 5, 6, 1, 31, 4, 8, 3, 11, 2, 17, 5, 7, 6, 6, 1, 37, 2, 19, 3, 13, 5, 8, 1, 41, 6, 7, 1, 43, 4, 11, 5, 9, 2, 23, 1, 47, 6, 8, 7

Offset: 1

Omar E. Pol, Jul 04 2009

Note that if n is a square then the square root of n appears repeated: i = j = sqrt(n).

Squarest (least oblong) integral rectangle with area n. This has minimal semiperimeter (A063655), since s = i + j = i + n/i is minimal when ds/di = 1 - n/i^2 = 0, i.e., n = i^2. - Daniel Forgues, Sep 29 2014

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Cf. A033676, A033677, A018253, A160812, A161344, A006446, A162190.

f[n_] := Block[{d = Divisors@n}, len = Length[d]/2; {d[[Ceiling@len]], d[[Floor[len + 1]] ]}]; f[1] = {1, 1}; Array[f, 49] // Flatten (* Robert G. Wilson v, Aug 17 2009 *)

a(35) and further terms from Robert G. Wilson v, Aug 17 2009; corrected Aug 18 2009

A162192 Triangle read by rows in which row n lists the divisors of n, prime(n), the consecutive composites that are greater than prime(n), and prime (n+1), but row 0 is formed by 1 and 2.

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 2, 3, 4, 5, 1, 3, 5, 6, 7, 1, 2, 4, 7, 8, 9, 10, 11, 1, 5, 11, 12, 13, 1, 2, 3, 6, 13, 14, 15, 16, 17, 1, 7, 17, 18, 19, 1, 2, 4, 8, 19, 20, 21, 22, 23, 1, 3, 9, 23, 24, 25, 26, 27, 28, 29, 1, 2, 5, 10, 29, 30, 31

Offset: 0

Omar E. Pol, Jun 30 2009

See also A162190, a sequence with a similar structure.

			Triangle begins:
1,(2);
1,(2),(3);
1,.2.,(3),4,(5);
1,.....3,...(5),6,(7);
1,.2,.....4,......(7),8,.9,10,(11);
1,...........5,...............(11),12,(13);
1,.2,..3,.......6,....................(13),14,15,16,(17);
1,.................7,...............................(17),18,(19);
1,.2,.....4,..........8,....................................(19),20,21,22,(23);

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

Cf. A000005, A000040, A000720, A027750, A018253, A160811, A160812, A161205, A161344, A161345, A161424, A006446, A161827, A161828, A161835, A162190.

cp's OEIS Frontend

A162348 List of pairs (i,j) of central factors of n, such that i*j = n, where i is the largest divisor of n <= sqrt(n) and j is the smallest divisor of n >= sqrt(n).

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