cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A387138 Triangle read by rows: T(n, k) = binomial(n, k) * Product_{k=1..n} radical(k), where radical(n) is the product of distinct prime factors of n, cf. A007947.

Original entry on oeis.org

1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 12, 48, 72, 48, 12, 60, 300, 600, 600, 300, 60, 360, 2160, 5400, 7200, 5400, 2160, 360, 2520, 17640, 52920, 88200, 88200, 52920, 17640, 2520, 5040, 40320, 141120, 282240, 352800, 282240, 141120, 40320, 5040
Offset: 0

Views

Author

Peter Luschny, Aug 18 2025

Keywords

Examples

			Triangle begins:
  [0]    1;
  [1]    1,     1;
  [2]    2,     4,      2;
  [3]    6,    18,     18,      6;
  [4]   12,    48,     72,     48,     12;
  [5]   60,   300,    600,    600,    300,     60;
  [6]  360,  2160,   5400,   7200,   5400,   2160,    360;
  [7] 2520, 17640,  52920,  88200,  88200,  52920,  17640,  2520;
  [8] 5040, 40320, 141120, 282240, 352800, 282240, 141120, 40320, 5040;
		

Crossrefs

Cf. A007318 (binomial), A007947 (radical), A048803 (column 0 and main diagonal), A387139 (row sums), A387126.

Programs

  • Maple
    A387138 := (n, k) -> binomial(n, k) * mul(NumberTheory:-Radical(j), j = 1..n):
  • Mathematica
    A387138[n_, k_] := Binomial[n, k] Times @@ ResourceFunction["IntegerRadical"][Range[1, n]];
    Table[A387138[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

Formula

T(n, k) = A048803(n) * A007318(n, k).
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