login
Numbers k such that phi(k) = number of perfect partitions of (k-1).
0

%I #11 Feb 29 2020 03:32:43

%S 1,2,4,8,16,20,32,64,112,128,256,512,1024,2048,2816,4096,8192,13312,

%T 16384,32768,65536,131072,262144,278528,524288,1000512,1048576,

%U 1245184,2097152,4194304,8388608,16777216,24117248,33554432,67108864

%N Numbers k such that phi(k) = number of perfect partitions of (k-1).

%C Numbers k such that A000010(k) = A002033(k-1).

%C Also numbers k such that A000010(k) = A074206(k). - _Amiram Eldar_, Feb 29 2020

%t f[1] = 1; f[n_] := f[n] = Plus @@ (f /@ Most @ Divisors[n]); Select[Range[1000], f[#] == EulerPhi[#] &] (* _Amiram Eldar_, Feb 29 2020 *)

%Y Cf. A000010, A002033, A074206.

%Y A000079 is a subsequence.

%K nonn,more

%O 1,2

%A _Juri-Stepan Gerasimov_, Oct 08 2009

%E Index in the definition corrected, and extended by _R. J. Mathar_, Oct 10 2009

%E a(18)-a(35) from _Amiram Eldar_, Feb 29 2020