OFFSET
1,1
COMMENTS
Observations:
The primes a(n)/4: {5, 17, 53, 4373, 13121, ...} are of the form 2*3^m - 1, m > 0 (A079363).
The primes a(n)/8: {5, 41, 293, 4941257, ...} are of the form 6*7^m - 1, m = 0, 1, ... (primes in A198688).
The set of the primes {a(n)/16} = {3, 11, 19, 59, 107, 179, 499, 971, 1499, 1619, ...} contains the primes of the form 4*3^(2m+1) - 1 = {11, 107, 971, ...}, m = 0, 1, ...
LINKS
Robert Israel, Table of n, a(n) for n = 1..738
MAPLE
with(numtheory):
for n from 2 by 2 to 10^6 do:
x:=divisors(n):n1:=nops(x):s0:=0:s1:=0:
for k from 1 to n1 do:
if type(x[k], even)
then
s0:=s0+ x[k]:
else
s1:=s1+ x[k]:
fi:
od:
if s1=lambda(s0)
then
printf(`%d, `, n):
else
fi:
od:
MATHEMATICA
fQ[n_] :=
Block[{d = Divisors@n},
CarmichaelLambda[Plus @@ Select[d, EvenQ]] ==
Plus @@ Select[d, OddQ]]; Select[2 Range@2000, fQ] (* Robert G. Wilson v, Oct 07 2017 *)
PROG
(PARI) is(n)=if(n%2, return(0)); my(s=valuation(n, 2), d=sigma(n>>s)); lcm(znstar(d*(2^(s+1)-2))[2])==d \\ Charles R Greathouse IV, Dec 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 07 2017
EXTENSIONS
Edited by Robert Israel, Dec 28 2017
STATUS
approved