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A293356
Even integers k such that lambda(sum of even divisors of k) = sum of odd divisors of k.
1
2, 20, 40, 48, 68, 176, 212, 304, 328, 944, 1360, 1712, 1888, 2320, 2344, 2864, 4240, 7120, 7888, 7984, 8448, 8960, 11920, 12032, 14416, 14592, 15536, 17492, 20224, 21520, 23984, 24208, 24592, 25904, 26112, 28160, 29440, 30464, 34560, 35920, 36352, 40528, 41296
OFFSET
1,1
COMMENTS
Or even integers k such that A002322(A146076(k)) = A000593(k).
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
EXAMPLE
68 is in the sequence because A002322(A146076(68) = A002322(108) = 18 and A000593(68) = 18.
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