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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
 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, 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, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,24 COMMENTS T(n, k) > 0 for all values of k iff n is practical (A005153). LINKS FORMULA T(n, n) = A033630(n). 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. EXAMPLE Table begins as: 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 1,0,0,0,0,0,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,0,1,1,0,0,0,0,1,1,0,1,1 1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1 MATHEMATICA 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 CROSSREFS Cf. A005153, A027750, A030057, A033630, A119348, A225561, A237287, A322860. Sequence in context: A193805 A159704 A101428 * A321787 A331596 A023586 Adjacent sequences:  A307220 A307221 A307222 * A307224 A307225 A307226 KEYWORD nonn,tabf AUTHOR Amiram Eldar, Mar 29 2019 STATUS approved

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Last modified May 10 22:11 EDT 2021. Contains 343780 sequences. (Running on oeis4.)