

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
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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



