login
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).
6
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, ...
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
Sequence in context: A341810 A338511 A332971 * A288501 A288019 A288442
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 07 2017
EXTENSIONS
a(18)-a(26) from Amiram Eldar, Mar 01 2020
STATUS
approved