A286265 Totient abundant numbers: numbers k such that A092693(k) > k.

5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 123, 125, 127, 131, 133, 137, 139, 141, 143, 145, 149, 151, 153, 155, 157

Offset: 1

Author

Amiram Eldar, May 05 2017

Keywords

• nonn

Examples

			19 is a totient abundant number since A092693(19) = phi(19) + phi(phi(19)) + ... = 18 + 6 + 2 + 1 = 27 > 19.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Paul Loomis and Florian Luca, On totient abundant numbers, Electronic Journal of Combinatorial Number Theory, Vol. 8, #A06 (2008).

Crossrefs

Cf. A000010, A082897, A092693.

Programs

Mathematica

totAbundantQ[n_] := Plus @@ FixedPointList[ EulerPhi@ # &, n] > 2*n+1; Select[Range[1000],totAbundantQ]

Python

from sympy import totient
def a092693(n): return 0 if n==1 else totient(n) + a092693(totient(n))
print([n for n in range(1, 201) if a092693(n) > n]) # Indranil Ghosh, May 05 2017