A069185 Numbers n such that n=phi(n)*core(n) where phi(x) is the Euler totient function and core(x) the squarefree part of x (the smallest integer such that x*core(x) is a square).

1, 2, 8, 12, 32, 48, 108, 128, 192, 432, 512, 768, 972, 1728, 2048, 3072, 3888, 6912, 8192, 8748, 12288, 15552, 27648, 32768, 34992, 49152, 62208, 78732, 110592, 131072, 139968, 196608, 248832, 314928, 442368, 524288, 559872, 708588, 786432, 995328, 1259712

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

{1} union {numbers of form 2^(2u+1)} union {numbers of form 4^(u+1)*3^(2v+1)} u, v>=0. - Benoit Cloitre, Aug 31 2004

Mathematica

f[p_, e_] := (p^e - p^(e - 1)) * p^Mod[e, 2]; aQ[1] = True; aQ[n_] := Times @@ (f @@@ FactorInteger[n]) == n; Select[Range[10000], aQ] (* Amiram Eldar, Aug 05 2019 *)

Crossrefs

Cf. A000010, A007913.

Sequence in context: A048074 A126775 A306898 * A037197 A125712 A062290

Adjacent sequences: A069182 A069183 A069184 * A069186 A069187 A069188

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 14 2002

Extensions

More terms from Amiram Eldar, Aug 05 2019

Status

approved