A207375 Irregular array read by rows in which row n lists the (one or two) central divisors of n in increasing order.

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

Offset

1,3

Comments

If n is a square then row n lists only the square root of n because the squares (A000290) have only one central divisor.

If n is not a square then row n lists the pair (j, k) of divisors of n, nearest to the square root of n, such that j*k = n.

Conjecture 1: It appears that the n-th record in this sequence is the last member of row A008578(n).

Column 1 gives A033676. Right border gives A033677. - Omar E. Pol, Feb 26 2019

The conjecture 1 follows from Bertrand's Postulate. - Charles R Greathouse IV, Feb 11 2022

Row products give A097448. - Omar E. Pol, Feb 17 2022

Links

Alois P. Heinz, Rows n = 1..5000

Omar E. Pol, Illustration of the divisors of the first 12 positive integers

Example

Array begins:
  1;
  1,  2;
  1,  3;
  2;
  1,  5;
  2,  3;
  1,  7;
  2,  4;
  3;
  2,  5;
  1, 11;
  3,  4;
  1, 13;
...

Crossrefs

Row n has length A169695(n).

Row sums give A207376.

Cf. A000005, A000290, A008578, A027750, A033676, A033677, A097448, A161901, A161904.

Sequence in context: A002335 A280738 A370628 * A173302 A251721 A251722

Adjacent sequences: A207372 A207373 A207374 * A207376 A207377 A207378

Keyword

nonn,tabf

Author

Omar E. Pol, Feb 23 2012

Status

approved