|
|
A076373
|
|
Solutions to n + 2*phi(n) = sigma(n) = n + 2*A000010(n) = A000203(n).
|
|
2
|
|
|
10, 44, 184, 752, 3796, 12224, 49024, 12580864, 60610624, 1091389696, 2936313088, 46672718384, 58082557696, 78857645056, 118480915456, 206158168064, 292776422368, 346109272672, 393960181792
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Is the number of solutions finite? Do solutions to n+k*phi(n)=sigma(n) exist for all values of k? For k=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 the number of solutions I know below 1000000 is {1, 7, 2, 2, 1, 5, 3, 3, 0, 1, 1}). Not more for larger k.
If 3*2^n-1 is prime for n>0, then 2^n(3*2^n-1) belongs to the sequence; therefore this sequence is infinite if the sequence of primes of the form 3*2^n-1 (A007505) is infinite. - Matthew Vandermast, Jul 31 2004
3796=4.13.73 and 60610624=64.199.4759 do not belong to the class of numbers mentioned above by Vandermast.
|
|
LINKS
|
|
|
EXAMPLE
|
n=44, phi(n)=20, sigma(44)=1+2+4+11+22+44=84=44+2*20
|
|
MATHEMATICA
|
ta={{0}}; k=2; Do[g=n; If[Equal[n+k*EulerPhi[n], DivisorSigma[1, n]], ta=Append[ta, n]; Print[n]], {n, 1, 182000000}]; {ta, g}
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|