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A339304 Irregular triangle read by rows T(n,k) in which row n has length the partition number A000041(n-1) and columns k give the number of divisors function A000005, 1 <= k <= n. 0
1, 2, 2, 1, 3, 2, 1, 2, 2, 2, 1, 1, 4, 3, 2, 2, 2, 1, 1, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 1, 4, 4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 3, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 4, 4, 2, 4, 4, 2, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(n,k) is also the number of divisors of A336811(n,k).

Conjecture: the sum of row n equals A138137(n), the total number of parts in the last section of the set of partitions of n.

LINKS

Table of n, a(n) for n=1..97.

FORMULA

a(m) = A000005(A336811(m)).

T(n,k) = A000005(A336811(n,k).

EXAMPLE

Triangle begins:

  1;

  2;

  2, 1;

  3, 2, 1;

  2, 2, 2, 1, 1;

  4, 3, 2, 2, 2, 1, 1;

  2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 1;

  4, 4, 2, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1;

  3, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1;

...

CROSSREFS

Number of divisors of A336811.

Row n has length A000041(n-1).

Every column gives A000005.

Row sums give A138137 (conjectured).

Cf. A135010, A138121, A138879, A187219.

Sequence in context: A281013 A190683 A181810 * A237578 A026146 A325519

Adjacent sequences:  A339301 A339302 A339303 * A339305 A339306 A339307

KEYWORD

nonn,tabf,new

AUTHOR

Omar E. Pol, Nov 29 2020

STATUS

approved

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Last modified January 17 23:09 EST 2021. Contains 340249 sequences. (Running on oeis4.)