A318490 Irregular triangle read by rows T(n,k): T(1,1) = 0; for n > 1, row n lists distinct prime factors of the n-th highly composite number (A002182(n)), where column k = 1, 2, 3, ..., omega(A002182(n)) = A108602(n).

0, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 11, 2, 3, 5, 7

Offset

1,2

Comments

The exponents of factors in row n are given by A212182(n).

Links

Peter J. Marko, Table of i, a(i) for i = 1..10022 (corresponding to first n = 584 rows of irregular triangle; using data from Flammenkamp)

A. Flammenkamp, Highly composite numbers

A. Flammenkamp, List of the first 1200 highly composite numbers

A. Flammenkamp, List of the first 779,674 highly composite numbers

Peter J. Marko, Table of n, T(n, k) by rows for n = 1..10000 (using data from Flammenkamp)

S. Ramanujan, Highly composite numbers, Proceedings of the London Mathematical Society, 2, XIV, 1915, 347 - 409.

Example

Triangle begins:
  0;
  2;
  2;
  2, 3;
  2, 3;
  2, 3;
  2, 3;
  2, 3;
  2, 3, 5;
  2, 3, 5;
  2, 3, 5;
  2, 3, 5;
  2, 3, 5;
  2, 3, 5;
  2, 3, 5, 7;
  ...
1st row: A002182(1) = 1 so T(1,1) = 0;
2nd row: A002182(2) = 2 so T(2,1) = 2;
3rd row: A002182(3) = 4 = 2^2 so T(3,1) = 2;
4th row: A002182(4) = 6 = 2 * 3 so T(4,1) = 2 and T(4,2) = 3;
5th row: A002182(5) = 12 = 2^2 * 3 so T(5,1) = 2 and T(5,2) = 3;
6th row: A002182(6) = 24 = 2^3 * 3 so T(6,1) = 2 and T(6,2) = 3.

Crossrefs

Row n has length A108602(n), n >= 2.

Cf. A000040, A002182, A212182.

Sequence in context: A258569 A091322 A252229 * A071215 A164024 A145193

Adjacent sequences: A318487 A318488 A318489 * A318491 A318492 A318493

Keyword

nonn,tabf

Author

Peter J. Marko, Aug 27 2018

Status

approved