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Numbers k such that k is the uphi(k)-th composite number, where uphi is the unitary totient function.
0

%I #20 Mar 20 2018 04:46:59

%S 6,12,15,21,24,28,36,52,68,76,265,295,2681,8104,21413,174757,1302197,

%T 15536176,20149241,25873648,237875719,358334927

%N Numbers k such that k is the uphi(k)-th composite number, where uphi is the unitary totient function.

%C The unitary version of A100410.

%C No more terms below 10^7.

%F Numbers k, such that k = A002808(A047994(k)).

%e 12 is a term because uphi(12) = 6 and 12 = A002808(6), the 6th composite.

%e 15 is a term because uphi(15) = 8 and 15 = A002808(8), the 8th composite.

%t uphi[n_] :=(Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n] ))[[1]] ; seqQ[n_] := (n - uphi[n] - 1 == PrimePi[n]); Select[Range[2,10^7], seqQ]

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

%o isok(k) = k - primepi(k) - 1 == uphi(k); \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A000720, A002808, A047994, A100410.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Mar 06 2018

%E a(18)-a(22) from _Robert G. Wilson v_, Mar 07 2018