|
|
A322162
|
|
Numbers k such that bsigma(k) = 2k + 2, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).
|
|
0
|
|
|
80, 104, 832, 1952, 7424, 62464, 522752, 8382464, 33357824, 134193152, 267649024, 17167286272, 549754241024
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
If m is a term of A050414, i.e., 2^m - 3 is prime, then 2^(2*m-2) * (2^m-3) is in this sequence, and also 2^(m-1) * (2^m-3) if m is even.
|
|
LINKS
|
|
|
EXAMPLE
|
80 is in this sequence since its sum of bi-unitary divisors is 162 = 2 * 80 + 2.
|
|
MATHEMATICA
|
fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; Select[Range[2, 10000], Times@@(fun @@@ FactorInteger[#]) == 2#+2 &]
|
|
PROG
|
(PARI) bsigma(n, f=factor(n))=prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if (e%2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|