|
|
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, 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
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|