A292033 Unitary phibonacci numbers: solutions k of the equation uphi(k) = uphi(k-1) + uphi(k-2), where uphi(k) is the unitary totient function (A047994).

3, 4, 7, 23, 9179, 244967, 14307856, 24571871, 128199059, 140830367, 401767631, 420567856, 468190439, 525970979, 780768167, 886434647, 1597167647, 4046753951, 4473784823, 5364666167, 5515718207, 11175736336, 14408460167, 18026319712, 20106993887, 20357733131

Offset

1,1

Comments

The unitary version of A065557. Common terms are 3, 7, 23, 9179, 244967, ... Terms that are not in A065557 are 4, 14307856, 420567856, ...

Links

Table of n, a(n) for n=1..26.

Example

uphi(14307856) = uphi(14307855) + uphi(14307854) (3366080 = 7102080 + 6264000), so 14307856 is in the sequence.

Mathematica

uphi[n_]:=If[n == 1, 1, (Times@@(Table[#[[1]]^#[[2]]-1, {1}] & /@ FactorInteger[n]))[[1]]]; Select[ Range[3, 10^6], uphi[#] == uphi[#-1] + uphi[#-2] &]

Prog

(PARI) uphi(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2]-1);
isok(n) = uphi(n)==uphi(n-1)+uphi(n-2); \\ Altug Alkan, Sep 08 2017

Crossrefs

Cf. A047994, A065557.

Sequence in context: A341810 A338511 A332971 * A288501 A288019 A288442

Adjacent sequences: A292030 A292031 A292032 * A292034 A292035 A292036

Keyword

nonn

Author

Amiram Eldar, Sep 07 2017

Extensions

a(18)-a(26) from Amiram Eldar, Mar 01 2020

Status

approved