A292033 - OEIS

%I #14 Mar 01 2020 04:40:40

%S 3,4,7,23,9179,244967,14307856,24571871,128199059,140830367,401767631,

%T 420567856,468190439,525970979,780768167,886434647,1597167647,

%U 4046753951,4473784823,5364666167,5515718207,11175736336,14408460167,18026319712,20106993887,20357733131

%N 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).

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

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

%t 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] &]

%o (PARI) uphi(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2]-1);

%o isok(n) = uphi(n)==uphi(n-1)+uphi(n-2); \\ _Altug Alkan_, Sep 08 2017

%Y Cf. A047994, A065557.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 07 2017

%E a(18)-a(26) from _Amiram Eldar_, Mar 01 2020