A364750 Integers k such that A000010(k) <= A008480(k).

1, 2, 6, 3326400, 4989600, 6652800, 9979200, 11793600, 19958400, 21621600, 23284800, 23587200, 25945920, 29937600, 33264000, 34927200, 35380800, 39916800, 43243200, 46569600, 47174400, 49896000, 51891840, 58968000, 59875200, 64864800, 66528000, 69854400, 70761600, 76204800, 77837760, 79833600

Offset: 1

Author

Michel Marcus, Aug 05 2023

Keywords

• nonn

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.

Crossrefs

Cf. A000010, A008480.

Programs

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 *)

PARI

m(n) = my(f=factor(n)[,2]); vecsum(f)!/prod(k=1, #f, f[k]!); \\ A008480
isok(n) = eulerphi(n) <= m(n);