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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).
3
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
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.
Sequence in context: A258569 A091322 A252229 * A071215 A164024 A145193
KEYWORD
nonn,tabf
AUTHOR
Peter J. Marko, Aug 27 2018
STATUS
approved