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

1,1

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

Links

Table of n, a(n) for n=1..62.

Mathematica

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

Crossrefs

Cf. A000010, A002033, A074206, A174090.

Sequence in context: A255130 A054021 A066191 * A169693 A180121 A331418

Adjacent sequences: A166156 A166157 A166158 * A166160 A166161 A166162

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 08 2009

Extensions

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

Status

approved