A333611 Sum of the iterated infinitary totient function iphi (A091732).

0, 1, 3, 6, 10, 3, 9, 6, 14, 10, 20, 9, 21, 9, 14, 29, 45, 14, 32, 21, 21, 20, 42, 9, 33, 21, 45, 32, 60, 14, 44, 29, 41, 45, 33, 33, 69, 32, 33, 21, 61, 21, 63, 44, 61, 42, 88, 44, 92, 33, 61, 69, 121, 45, 61, 32, 69, 60, 118, 33, 93, 44, 92, 106, 92, 41, 107

Offset: 1

Author

Amiram Eldar, Mar 28 2020

Keywords

• nonn

Examples

			a(3) = iphi(3) + iphi(iphi(3)) = 2 + 1 = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A091732, A092693, A329153, A330273, A331273, A333609.

Programs

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); a[n_] := Plus @@ NestWhileList[iphi, n, # != 1 &] - n; Array[a, 100]