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
Examples
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.
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.
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