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A253196 Irregular array read by rows. T(n,k) is the number of divisors d of n such that k^2 is the greatest square that divides d, n>=1, 1<=k<=A000188(n). 1
1, 2, 2, 2, 1, 2, 4, 2, 2, 2, 2, 0, 1, 4, 2, 4, 2, 2, 4, 4, 2, 2, 0, 1, 2, 4, 0, 2, 2, 4, 2, 4, 4, 2, 4, 4, 2, 0, 0, 0, 1, 4, 2, 0, 2, 4, 2, 2, 8, 2, 2, 2, 0, 2, 4, 4, 4, 4, 2, 2, 0, 0, 1, 2, 4, 4, 4, 4, 2, 8, 2, 4, 2, 4, 0, 2, 4, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 2, 4, 4, 2, 2, 4, 0, 4, 4, 4, 4, 4, 4, 2, 8, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Row sums are A000005.
Column 1 is A034444.
LINKS
FORMULA
Dirichlet g.f. for column k: 1/k^(2*s) * zeta(s)^2/zeta(2*s).
EXAMPLE
1
2
2
2,1
2
4
2
2,2
2,0,1
4
2
4,2
2
4
4
2,2,0,1
2
4,0,2
For n=18, The divisors are: 1,2,3,6,9,18. T(18,1)=4 because 1 is the largest square that divides 1,2,3,6. T(18,3) = 2 because 9 is the largest square that divides 9,18.
MAPLE
with(numtheory):
T:= n-> (p-> seq(coeff(p, x, j), j=1..degree(p)))(add(
x^mul(i[1]^iquo(i[2], 2), i=ifactors(d)[2]), d=divisors(n))):
seq(T(n), n=1..70); # Alois P. Heinz, Mar 25 2015
MATHEMATICA
nn = 60; g[list_] := list /. {j___, 0 ...} -> {j}; f[list_, i_] := list[[i]]; Map[g, Transpose[Table[a = Table[If[n == k^2, 1, 0], {n, 1, nn}]; b = Table[2^PrimeNu[n], {n, 1, nn}]; Table[DirichletConvolve[f[a, n], f[b, n], n, m], {m, 1, nn}], {k, 1, nn}]]] // Grid
CROSSREFS
Sequence in context: A263923 A331248 A361913 * A353981 A271205 A303841
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Mar 24 2015
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)