|
%I #18 Mar 26 2023 02:19:50
%S 2,36,383,3708,35731,347505,3407290,33579303,332026623,3290205509
%N Number of totient abundant numbers <= 10^n.
%C Totient abundant numbers are defined in A286265.
%C a(3)-a(8) were calculated by Loomis & Luca (2008).
%H Paul Loomis and Florian Luca, <a href="https://www.emis.de/journals/INTEGERS/papers/i6/i6.Abstract.html">On totient abundant numbers</a>, Electronic Journal of Combinatorial Number Theory, Vol. 8, #A06 (2008).
%e There are 2 totient abundant numbers <= 10^1 (5 and 7), thus a(1)=2.
%t 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 *)
%o (PARI) s(n) = {n=eulerphi(n); if(n==1, 1, n+s(n));}
%o 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
%Y Cf. A000010, A082897, A092693, A286265.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, May 05 2017
%E a(9)-a(10) from _Amiram Eldar_, Mar 26 2023
|
