A300479 Numbers k such that k is the uphi(k)-th composite number, where uphi is the unitary totient function.

6, 12, 15, 21, 24, 28, 36, 52, 68, 76, 265, 295, 2681, 8104, 21413, 174757, 1302197, 15536176, 20149241, 25873648, 237875719, 358334927

Offset

1,1

Comments

The unitary version of A100410.

No more terms below 10^7.

Links

Table of n, a(n) for n=1..22.

Formula

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

Example

12 is a term because uphi(12) = 6 and 12 = A002808(6), the 6th composite.
15 is a term because uphi(15) = 8 and 15 = A002808(8), the 8th composite.

Mathematica

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]

Prog

(PARI) uphi(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[1, 2]-1);
isok(k) = k - primepi(k) - 1 == uphi(k); \\ Michel Marcus, Mar 07 2018

Crossrefs

Cf. A000720, A002808, A047994, A100410.

Sequence in context: A106420 A308611 A315619 * A315620 A315621 A315622

Adjacent sequences: A300476 A300477 A300478 * A300480 A300481 A300482

Keyword

nonn,more

Author

Amiram Eldar, Mar 06 2018

Extensions

a(18)-a(22) from Robert G. Wilson v, Mar 07 2018

Status

approved