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

0,5

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

Formula

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

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A007318, A046523.

Diagonals: A000012, A046523, A278253, A278252.

Sequence in context: A174842 A156074 A051287 * A216031 A263985 A176261

Adjacent sequences: A278215 A278216 A278217 * A278219 A278220 A278221

Keyword

nonn,tabl

Author

Antti Karttunen, Nov 19 2016

Status

approved