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