|
|
A344272
|
|
a(n) is the least k such that the average number of nonunitary divisors of {1..k} is >= n.
|
|
2
|
|
|
54, 816, 10530, 135200, 1733760, 22216752, 284685408, 3647978320, 46745561100, 599002268832, 7675674748560
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Lim_{n->oo} a(n+1)/a(n) = exp(1/(1-1/zeta(2))) = exp(Pi^2/(Pi^2-6)) = 12.8140996101...
|
|
EXAMPLE
|
a(1) = 54 since the average of the number of nonunitary divisors of {1..54} is (Sum_{k=1..54} A056175(k))/54 = 1.
|
|
MATHEMATICA
|
nd[n_] := DivisorSigma[0, n] - 2^PrimeNu[n]; seq={}; s = 0; k = 1; Do[While[s = s + nd[k]; s < k*n, k++]; AppendTo[seq, k]; k++, {n, 1, 5}]; seq
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|