|
|
A295830
|
|
Bi-unitary pseudoperfect numbers that equal to the sum of a subset of their aliquot bi-unitary divisors in a single way.
|
|
3
|
|
|
6, 60, 72, 78, 80, 88, 90, 102, 104, 114, 138, 150, 162, 174, 186, 222, 246, 258, 282, 294, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 704, 726, 762, 786, 822, 832, 834, 894, 906, 942, 978, 1002, 1014, 1038, 1074, 1086, 1146
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
72 is in the sequence since its aliquot bi-unitary divisors are 1, 2, 4, 8, 9, 18, 36 and {1, 8, 9, 18, 36} is the only subset whose sum is 72.
|
|
MATHEMATICA
|
f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; a={}; n=0; While[Length[a]<100, n++; d=Most[bdiv[n]]; c = SeriesCoefficient[ Series[ Product[1+x^d[[i]], {i, Length[d]}], {x, 0, n}], n ]; If[c==1; AppendTo[a, n]]]; a
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|