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A300479 Numbers k such that k is the uphi(k)-th composite number, where uphi is the unitary totient function. 0
6, 12, 15, 21, 24, 28, 36, 52, 68, 76, 265, 295, 2681, 8104, 21413, 174757, 1302197, 15536176, 20149241, 25873648, 237875719, 358334927 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 29 05:41 EDT 2022. Contains 354122 sequences. (Running on oeis4.)