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(k)/phi(k) = 1, 1, 1, 3/2 for k = 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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 19 2017
STATUS
approved