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

Author

Amiram Eldar, Sep 07 2017

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A047994, A065557.

Programs

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] &]

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

Extensions

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