A307223 - OEIS

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).

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

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OFFSET

1,24

COMMENTS

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

LINKS

Table of n, a(n) for n=1..87.

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

1,0,1,1

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: A101428 A360171 A348528 * A321787 A331596 A023586

Adjacent sequences: A307220 A307221 A307222 * A307224 A307225 A307226

KEYWORD

nonn,tabf

AUTHOR

Amiram Eldar, Mar 29 2019

STATUS

approved