A166159 Numbers k such that phi(k) + number of perfect partitions of (k-1) = k.

2, 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 19, 23, 29, 31, 32, 37, 41, 43, 47, 53, 59, 60, 61, 64, 67, 71, 73, 79, 80, 83, 89, 97, 101, 103, 107, 109, 113, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 08 2009

Keywords

• nonn

Comments

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

Also numbers k such that A000010(k) + A074206(k) = k. Union of the primes (A000040), the powers of 2 (A000079) above 1, and the terms 12, 60, 80, 448, 528, 560, 3648, 4560, 11264, 22272, 24320, 53248, 125952, 146432, 1114112, 3489792, 3850240, 4145152, 4980736, 12931072, 17498112, 19333120, 20905984, 21168128, 85721088, 96468992, ... - Amiram Eldar, Feb 29 2020

Crossrefs

Cf. A000010, A002033, A074206, A174090.

Programs

Mathematica

f[1] = 1; f[n_] := f[n] = Plus @@ (f /@ Most @ Divisors[n]); Select[Range[1000], f[#] + EulerPhi[#] == # &] (* Amiram Eldar, Feb 29 2020 *)

Extensions

Index in the definition corrected, and extended by R. J. Mathar, Oct 10 2009