login
A166159
Numbers k such that phi(k) + number of perfect partitions of (k-1) = k.
0
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
MATHEMATICA
f[1] = 1; f[n_] := f[n] = Plus @@ (f /@ Most @ Divisors[n]); Select[Range[1000], f[#] + EulerPhi[#] == # &] (* Amiram Eldar, Feb 29 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Index in the definition corrected, and extended by R. J. Mathar, Oct 10 2009
STATUS
approved