A286266 Number of totient abundant numbers <= 10^n.

2, 36, 383, 3708, 35731, 347505, 3407290, 33579303, 332026623, 3290205509

Offset: 1

Author

Amiram Eldar, May 05 2017

Keywords

• nonn
• more

Comments

Totient abundant numbers are defined in A286265.

a(3)-a(8) were calculated by Loomis & Luca (2008).

Examples

			There are 2 totient abundant numbers <= 10^1 (5 and 7), thus a(1)=2.
		

Links

• Paul Loomis and Florian Luca, On totient abundant numbers, Electronic Journal of Combinatorial Number Theory, Vol. 8, #A06 (2008).

Crossrefs

Cf. A000010, A082897, A092693, A286265.

Programs

Mathematica

Accumulate@ Table[Count[Select[Range[10^(n - 1) + 1, 10^n], (Total@ FixedPointList[EulerPhi, #] - (# + 1)) > # &], k_ /; k <= 10^n], {n, 6}] (* Michael De Vlieger, May 06 2017, after Alonso del Arte at A092693 *)

PARI

s(n) = {n=eulerphi(n); if(n==1, 1, n+s(n));}
lista(nmax) = {my(c = 0, r = 10); for(k = 1, 10^nmax, if(s(k) > k, c++); if(k == r, print1(c, ", "); r *= 10));} \\ Amiram Eldar, Mar 26 2023

Extensions

a(9)-a(10) from Amiram Eldar, Mar 26 2023