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A307223 Irregular table T(n, k) read by rows: n-th row gives number of subsets of the divisors of n which sum to k for 1 <= k <= sigma(n). 2

%I

%S 1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,

%T 0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,1,1,0,1,

%U 1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1

%N Irregular table T(n, k) read by rows: n-th row gives number of subsets of the divisors of n which sum to k for 1 <= k <= sigma(n).

%C T(n, k) > 0 for all values of k iff n is practical (A005153).

%F T(n, n) = A033630(n).

%F T(n, A030057(n)) = 0 if there is a 0 in the n-th row, i.e. A030057(n) <= sigma(n) or n is not practical.

%e Table begins as:

%e 1

%e 1,1,1

%e 1,0,1,1

%e 1,1,1,1,1,1,1

%e 1,0,0,0,1,1

%e 1,1,2,1,1,2,1,1,2,1,1,1

%e 1,0,0,0,0,0,1,1

%e 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%e 1,0,1,1,0,0,0,0,1,1,0,1,1

%e 1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1

%t T[n_,k_] := Module[{d = Divisors[n]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, k}], k]]; Table[T[n, k], {n,1,10}, {k, 1, DivisorSigma[1,n]}] // Flatten

%Y Cf. A005153, A027750, A030057, A033630, A119348, A225561, A237287, A322860.

%K nonn,tabf

%O 1,24

%A _Amiram Eldar_, Mar 29 2019

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Last modified May 18 04:58 EDT 2021. Contains 343994 sequences. (Running on oeis4.)