OFFSET
1,2
COMMENTS
Cameron asked whether there is an integer k with exactly 3 distinct prime factors such that A000010(k) < A008480(k). David Bevan found that the smallest example is 2^51 * 3^34 * 5^20 = 3.581...*10^45. - Amiram Eldar, Aug 06 2023
LINKS
Peter Cameron's Blog, An exercise in number theory, Posted on 17/02/2023.
MATHEMATICA
g[p_, e_] := (p - 1)*p^(e - 1); q[n_] := Module[{f = FactorInteger[n]}, Times @@ g @@@ f <= Multinomial @@ f[[;; , 2]]]; Select[Range[10^7], q] (* Amiram Eldar, Aug 06 2023 *)
PROG
(PARI) m(n) = my(f=factor(n)[, 2]); vecsum(f)!/prod(k=1, #f, f[k]!); \\ A008480
isok(n) = eulerphi(n) <= m(n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 05 2023
STATUS
approved