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A249716 The least nonsquarefree number on row n of Pascal's triangle, or 1 if all the terms on that row are squarefree. 5
1, 1, 1, 1, 4, 1, 20, 1, 8, 9, 45, 1, 12, 1287, 364, 6435, 16, 136, 18, 171, 20, 5985, 1540, 1, 24, 25, 325, 27, 28, 3654, 4060, 169911, 32, 528, 5984, 52360, 36, 666, 8436, 82251, 40, 820, 11480, 145008513, 44, 45, 1035, 12551759587422, 48, 49, 50, 1275, 52, 292825, 54, 1485, 56, 1596, 30856, 45057474, 60, 55525372, 37820, 63, 64, 2080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

After a(0) = 1, A048278 gives the positions of seven other ones in the sequence.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = binomial(n, A249442(n)).

EXAMPLE

           Binomial coefficients     First squarefree     a(n)

                 A007318             occurs at index?      =

----------------------------------------------------------------------------

Row 0                1               no squarefrees        1 (by definition)

Row 1              1   1             no squarefrees        1

Row 2            1   2   1           no squarefrees        1

Row 3          1   3   3   1         no squarefrees        1

Row 4        1   4   6   4   1              1              4

Row 5      1   5  10  10   5   1     no squarefrees        1

Row 6    1   6  15  20  15   6   1          3             20

PROG

(PARI)

A249716(n) = { my(b); for(k=0, n\2, if(0==moebius(b=binomial(n, k)), return(b))); return(1); }

for(n=0, 10000, write("b249716.txt", n, " ", A249716(n)));

(Scheme) (define (A249716 n) (A007318tr n (A249442 n)))

CROSSREFS

A249717 and A249718 give the smallest and the largest prime whose square divides these numbers.

Cf. also A007318, A005117, A013929, A048277, A048278, A249442.

Sequence in context: A057968 A141233 A055139 * A333273 A128041 A144885

Adjacent sequences:  A249713 A249714 A249715 * A249717 A249718 A249719

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 04 2014

STATUS

approved

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)