|
|
A274628
|
|
Nathanson's orphan-counting function h(n).
|
|
3
|
|
|
1, 4, 7, 13, 15, 26, 25, 39, 40, 54, 49, 79, 63, 88, 88, 112, 93, 140, 109, 159, 142, 170, 143, 224, 168, 216, 202, 255, 199, 304, 219, 308, 268, 316, 274, 404, 281, 370, 338, 438, 323, 484, 345, 481, 433, 484, 389, 611, 422, 566, 492, 607, 459, 684, 508, 692
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Number of integer solutions to a*b - c*d = n such that a > c >= 0 and b > d >= 0. - David Radcliffe, Mar 28 2019
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Sum_{i,j>=1} x^(i*j)/((1-x^i)*(1-x^j)). - Seiichi Manyama, Jan 08 2022
|
|
MATHEMATICA
|
Table[Total[Function[parts, Count[CountDistinct /@ IntegerPartitions[n, All, parts], 2]] /@ Subsets[Range[n], {2}]] + 2 DivisorSigma[1, n] - DivisorSigma[0, n], {n, 1, 100}] (* Eric Rowland, May 26 2018 *)
|
|
PROG
|
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(i=1, N, sum(j=1, N\i, x^(i*j)/((1-x^i)*(1-x^j))))) \\ Seiichi Manyama, Jan 08 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|