login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A283052 Numbers n such that uphi(n)/phi(n) > uphi(m)/phi(m) for all m < n, where phi(n) is the Euler totient function (A000010) and uphi(n) is the unitary totient function (A047994). 1
1, 4, 8, 16, 32, 36, 72, 144, 216, 288, 432, 864, 1728, 2592, 3600, 5400, 7200, 10800, 21600, 43200, 64800, 108000, 129600, 216000, 259200, 324000, 529200, 1058400, 2116800, 3175200, 5292000, 6350400, 10584000, 12700800, 15876000, 31752000, 63504000, 95256000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is infinite.

a(1) = 1, a(6) = 36, a(15) = 3600 and a(32) = 6350400 are the smallest numbers n such that uphi(n)/phi(n) = 1, 2, 3 and 4. They are squares of 1, 6, 60, and 2520.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..46

EXAMPLE

uphi(n)/phi(n) = 1, 1, 1, 3/2 for n = 1, 2, 3, 4, thus a(1) = 1 and a(2) = 4 since a(4) > a(m) for m < 4.

MATHEMATICA

uphi[n_] := If[n == 1, 1, (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@

FactorInteger[n]))[[1]]]; a = {}; rmax = 0; For[k = 0, k < 10^9, k++; r = uphi[k]/EulerPhi[k]; If[r > rmax, rmax = r; a = AppendTo[a, k]]]; a

PROG

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

lista(nn) = {my(rmax = 0); for (n=1, nn, if ((newr=uphi(n)/eulerphi(n)) > rmax, print1(n, ", "); rmax = newr); ); } \\ Michel Marcus, May 20 2017

CROSSREFS

Cf. A000010, A047994, A285906.

Sequence in context: A075090 A304250 A322793 * A088259 A123857 A217313

Adjacent sequences:  A283049 A283050 A283051 * A283053 A283054 A283055

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 19 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 17 18:37 EST 2020. Contains 332005 sequences. (Running on oeis4.)