A249716 The least nonsquarefree number on row n of Pascal's triangle, or 1 if all the terms on that row are squarefree.

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

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: A141233 A055139 A349708 * A333273 A128041 A144885

Adjacent sequences: A249713 A249714 A249715 * A249717 A249718 A249719

Keyword

nonn

Author

Antti Karttunen, Nov 04 2014

Status

approved