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A271187 Triangle T(n,k) read by rows: T(n,k) is the squarefree part of C(n,k). 1
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 6, 1, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 5, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 2, 7, 14, 70, 14, 7, 2, 1, 1, 1, 1, 21, 14, 14, 21, 1, 1, 1, 1, 10, 5, 30, 210, 7, 210, 30, 5, 10, 1, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 1, 3, 66, 55, 55, 22, 231, 22, 55, 55, 66, 3, 1, 1, 13, 78, 286, 715, 143, 429, 429, 143, 715, 286, 78, 13, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..104.

EXAMPLE

Triangle starts:

[1]

[1, 1]

[1, 2, 1]

[1, 3, 3, 1]

[1, 1, 6, 1, 1]

[1, 5, 10, 10, 5, 1]

[1, 6, 15, 5, 15, 6, 1]

[1, 7, 21, 35, 35, 21, 7, 1]

[1, 2, 7, 14, 70, 14, 7, 2, 1]

[1, 1, 1, 21, 14, 14, 21, 1, 1, 1]

[1, 10, 5, 30, 210, 7, 210, 30, 5, 10, 1]

[1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1]

[1, 3, 66, 55, 55, 22, 231, 22, 55, 55, 66, 3, 1]

[1, 13, 78, 286, 715, 143, 429, 429, 143, 715, 286, 78, 13, 1]

[1, 14, 91, 91, 1001, 2002, 3003, 858, 3003, 2002, 1001, 91, 91, 14, 1]

[1, 15, 105, 455, 1365, 3003, 5005, 715, 715, 5005, 3003, 1365, 455, 105, 15, 1]

...

MAPLE

T:= (n, k)-> mul(i[1]^irem(i[2], 2),

     i=ifactors(binomial(n, k))[2]):

seq(seq(T(n, k), k=0..n), n=0..15);  # Alois P. Heinz, Apr 01 2016

MATHEMATICA

Table[Times @@ Apply[Power, {First@ #, Mod[Last@ #, 2]} & /@ FactorInteger@ Binomial[n, k], {1}], {n, 0, 13}, {k, 0, n}] // Flatten (* Michael De Vlieger, Apr 01 2016, after Zak Seidov at A007913 *)

PROG

(PARI) for(n=0, 20, for(k=0, n, print1(core(binomial(n, k)), ", ")));

(MAGMA) /* As triangle: */ [[Squarefree(Binomial(n, k)): k in [0..n]]: n in [0..20]]; // Wesley Ivan Hurt, Apr 01 2016

(Sage) [squarefree_part(binomial(n, k)) for n in (0..15) for k in (0..n) ] # Bruno Berselli, Apr 01 2016

CROSSREFS

Cf. A007318 (binomial coefficients), A007913 (squarefree parts).

T(2n,n) gives A069113.

Sequence in context: A117185 A129181 A157694 * A093557 A098802 A048804

Adjacent sequences:  A271184 A271185 A271186 * A271188 A271189 A271190

KEYWORD

nonn,tabl

AUTHOR

Joerg Arndt, Apr 01 2016

STATUS

approved

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Last modified August 12 04:57 EDT 2020. Contains 336436 sequences. (Running on oeis4.)