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A278218 Triangle read by rows: T(n,k) = Least number with the prime signature of binomial(n,k). 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)