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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 Alois P. Heinz, Rows n = 1..6000, flattened 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 Cf. A000005, A000188, A034444. Sequence in context: A029330 A132225 A263923 * A271205 A303841 A093116 Adjacent sequences:  A253193 A253194 A253195 * A253197 A253198 A253199 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Mar 24 2015 STATUS approved

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Last modified October 22 10:50 EDT 2018. Contains 316436 sequences. (Running on oeis4.)