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A277648
Triangle T(n,k) = A277647(n, A005117(k)), read by rows.
8
1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 5, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1
OFFSET
1,2
COMMENTS
The columns of this triangle are the columns of A277647 with squarefree index.
Other that the first (with length 1), row n has length A278100(n).
FORMULA
T(n,k) = A000196(A277646(n,A005117(k))).
T(n,k) sqrt(A005117(k)) <= n < (T(n,k)+1) sqrt(A005117(k)).
EXAMPLE
Triangle begins:
1;
2, 1, 1;
3, 2, 1, 1, 1, 1;
4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1;
...
where the first 11 terms of A005117(k) are
1, 2, 3, 5, 6, 7,10,11,13,14,15.
MATHEMATICA
DeleteCases[#, 0] & /@ Table[Boole[SquareFreeQ@ k] Floor[n/Sqrt@ k], {n, 8}, {k, n^2}] (* Michael De Vlieger, Nov 24 2016 *)
PROG
(Magma)
A277647:=func<n, k|Isqrt(n^2 div k)>;
A277648_row:=func<n|[A277647(n, k):k in[1..n^2]|IsSquarefree(k)]>;
&cat[A277648_row(n):n in[1..8]];
(PARI)
row(n)={apply(k->sqrtint(n^2\k), select(issquarefree, [1..n^2]))}
for(n=1, 6, print(row(n))) \\ Andrew Howroyd, Feb 28 2018
CROSSREFS
Sequence in context: A374683 A211028 A239001 * A026792 A334301 A139100
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Nov 10 2016
EXTENSIONS
Missing a(3009) in b-file inserted by Andrew Howroyd, Feb 28 2018
STATUS
approved