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

%I A278218 #23 Nov 22 2016 21:48:06
%S A278218 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,
%T A278218 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,
%U A278218 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
%N A278218 Triangle read by rows: T(n,k) = Least number with the prime signature of binomial(n,k).
%H A278218 Antti Karttunen, <a href="/A278218/b278218.txt">Table of n, a(n) for n = 0..7259; first 120 antidiagonals</a>
%H A278218 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A278218 T(n,k) = A046523(C(n,k)).
%F A278218 a(n) = A046523(A007318(n)). [When viewed as a one-dimensional sequence.]
%e A278218 The triangle begins as:
%e A278218                                  1
%e A278218                               1,    1
%e A278218                             1,   2,   1
%e A278218                          1,   2,    2,   1
%e A278218                        1,   4,   6,   4,   1
%e A278218                     1,   2,   6,    6,   2,  1
%e A278218                   1,   6,   6,  12,   6,   6,  1
%e A278218                 1,  2,   6,   6,    6,   6,  2,  1
%e A278218               1,  8,  12,  24,  30,  24,  12,  8,  1
%e A278218             1,  4, 36,  60,  60,   60,  60, 36,  4,  1
%e A278218           1,  6, 12, 120, 210, 180, 210, 120, 12,  6,  1
%e A278218         1,  2,  6, 30, 210, 210,  210, 210, 30,  6,  2,  1
%e A278218       1, 12, 30, 60,  60, 360, 420, 360,  60, 60, 30, 12,  1
%e A278218     1,  2, 30, 30, 30,  60, 420,  420,  60, 30, 30, 30,  2,  1
%e A278218   1,  6,  6, 60, 30, 210, 210, 840, 210, 210, 30, 60,  6,  6,  1
%e A278218     etc.
%t A278218 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 *)
%o A278218 (Scheme) (define (A278218 n) (A046523 (A007318 n)))
%Y A278218 Cf. A007318, A046523.
%Y A278218 Diagonals: A000012, A046523, A278253, A278252.
%K A278218 nonn,tabl
%O A278218 0,5
%A A278218 _Antti Karttunen_, Nov 19 2016