A253473 a(n) = phi(c(n)) - tau(phi(c(n))), where c(n) is the n-th composite number.

0, 0, 1, 2, 1, 1, 2, 4, 4, 2, 4, 6, 6, 4, 14, 6, 12, 6, 4, 11, 14, 11, 16, 6, 12, 16, 11, 6, 14, 16, 18, 11, 34, 14, 26, 16, 12, 32, 16, 27, 22, 11, 22, 27, 26, 38, 14, 26, 38, 16, 16, 27, 32, 27, 48, 16, 26, 46, 32, 16, 57, 34, 48, 32, 16, 60, 38, 48, 42, 60

Offset: 1

Author

Carlos Eduardo Olivieri, Jan 02 2015

Keywords

• nonn
• easy

Examples

			For n=1: c(1) = 4. phi(4) = 2. tau(2)= 2, thus a(1) = 2 - 2 = 0.
For n=3: c(3) = 8. phi(8) = 4. tau(4)= 3, thus a(3) = 4 - 3 = 1.
For n=20: c(20) = 32. phi(32) = 16. tau(16) = 5, thus a(20) = 16 - 5 = 11.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• J. Ziegenbalg, Phi, Tau, Sigma in Elementary Number Theory

Crossrefs

Cf. A000005, A000010, A002808.

Programs

Maple

comps:= remove(isprime, [$2..1000]):
map( ((t->t) - numtheory:-tau)@numtheory:-phi, comps); # Robert Israel, Nov 20 2016

Mathematica

Composites := Select[Range[2, 10000], ! PrimeQ[#] &]; Composite[n_] := Last[Take[Composites, n]]; T[n_] := EulerPhi[n]; Table[T[Composite[n]] - DivisorSigma[0, T[Composite[n]]], {n, 200}]
EulerPhi[#]-DivisorSigma[0,EulerPhi[#]]&/@Select[Range[300],CompositeQ] (* Harvey P. Dale, Oct 05 2019 *)

PARI

lista(nn) = {forcomposite(n=1, nn, ec = eulerphi(n); print1(ec - numdiv(ec), ", "););} \\ Michel Marcus, Jan 11 2015

Formula

a(n) = A049820(A073256(n)). - Michel Marcus, Jan 08 2015

a(n) = A000010(A002808(n)) - A000005(A000010(A002808(n))). - Omar E. Pol, Nov 20 2016

Extensions

Name clarified by Omar E. Pol, Nov 20 2016