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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
OFFSET
0,5
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
Sequence in context: A174842 A156074 A051287 * A216031 A263985 A176261
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Nov 19 2016
STATUS
approved