A278218 Triangle read by rows: T(n,k) = Least number with the prime signature of binomial(n,k).

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 6, 4, 1, 1, 2, 6, 6, 2, 1, 1, 6, 6, 12, 6, 6, 1, 1, 2, 6, 6, 6, 6, 2, 1, 1, 8, 12, 24, 30, 24, 12, 8, 1, 1, 4, 36, 60, 60, 60, 60, 36, 4, 1, 1, 6, 12, 120, 210, 180, 210, 120, 12, 6, 1, 1, 2, 6, 30, 210, 210, 210, 210, 30, 6, 2, 1, 1, 12, 30, 60, 60, 360, 420, 360, 60, 60, 30, 12, 1

Offset: 0

Author

Antti Karttunen, Nov 19 2016

Keywords

• nonn
• tabl

Examples

			The triangle begins as:
                                 1
                              1,    1
                            1,   2,   1
                         1,   2,    2,   1
                       1,   4,   6,   4,   1
                    1,   2,   6,    6,   2,  1
                  1,   6,   6,  12,   6,   6,  1
                1,  2,   6,   6,    6,   6,  2,  1
              1,  8,  12,  24,  30,  24,  12,  8,  1
            1,  4, 36,  60,  60,   60,  60, 36,  4,  1
          1,  6, 12, 120, 210, 180, 210, 120, 12,  6,  1
        1,  2,  6, 30, 210, 210,  210, 210, 30,  6,  2,  1
      1, 12, 30, 60,  60, 360, 420, 360,  60, 60, 30, 12,  1
    1,  2, 30, 30, 30,  60, 420,  420,  60, 30, 30, 30,  2,  1
  1,  6,  6, 60, 30, 210, 210, 840, 210, 210, 30, 60,  6,  6,  1
    etc.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..7259; first 120 antidiagonals
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A007318, A046523.

Diagonals: A000012, A046523, A278253, A278252.

Programs

Mathematica

Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ Binomial[n, k]], {n, 0, 12}, {k, 0, n}] // Flatten (* Michael De Vlieger, Nov 21 2016 *)

Scheme

(define (A278218 n) (A046523 (A007318 n)))

Formula

T(n,k) = A046523(C(n,k)).

a(n) = A046523(A007318(n)). [When viewed as a one-dimensional sequence.]