A255686 Numbers n such that lambda(sum of odd divisors of Fibonacci(n)) = lambda(sum of even divisors of Fibonacci(n)) where lambda is the Carmichael function (A002322).

3, 9, 12, 15, 18, 21, 27, 33, 39, 45, 51, 63, 69, 87, 93, 111, 123, 135, 141, 153, 159, 177, 189, 201, 219, 225, 237, 249, 255, 267, 291, 303, 309, 321, 339, 363, 381, 393, 411, 423, 453, 459, 501, 537, 543, 573, 579, 633, 669, 699

Offset

1,1

Comments

Number n such that A002322(A193293(n))= A002322(A193294(n)).

a(n) is divisible by 3, and a majority of numbers a(n)/3 are primes: 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 47, 53, 59, 67, 73, 79, 83, 89, 97, 101, 103, 107, 113, 127, 131, 137, 151, 167, 179, 181, 191, 193, 211, 223, 233, ... The nonprimes a(n)/3 are 1, 4, 6, 9, 15, 21, 45, 51, 63, 75, 121, 153, ...

Links

Table of n, a(n) for n=1..50.

Example

18 is in the sequence because A002322(A193293(18)) = A002322(360) = 12 and A002322(A193294(18))= A002322(5040) = 12.

Mathematica

f[x_] := Plus @@ Select[Divisors[Fibonacci[x]], OddQ[#] &]; g[x_] := Plus @@ Select[Divisors[Fibonacci[x]], EvenQ[#]&]; Do[If[CarmichaelLambda[f[n]]== CarmichaelLambda[g[n]], Print[n]], {n, 1, 500}]

Prog

(PARI) a002322(n) = lcm(znstar(n)[2]);
isok(n) = my(fn = fibonacci(n)); my(sod = sumdiv(fn, d, d*(d%2))); my(sed = sigma(fn) - sod); sod && sed && (a002322(sod) == a002322(sed)); \\ Michel Marcus, Mar 02 2015

Crossrefs

Cf. A000045, A002322, A193293, A193294.

Sequence in context: A073536 A077468 A089425 * A138921 A194412 A136290

Adjacent sequences: A255683 A255684 A255685 * A255687 A255688 A255689

Keyword

nonn

Author

Michel Lagneau, Mar 02 2015

Status

approved