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

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

J. Ziegenbalg, Phi, Tau, Sigma in Elementary Number Theory

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000005, A000010, A002808.

Sequence in context: A096470 A085143 A321029 * A026120 A108746 A333270

Adjacent sequences: A253470 A253471 A253472 * A253474 A253475 A253476

Keyword

nonn,easy

Author

Carlos Eduardo Olivieri, Jan 02 2015

Extensions

Name clarified by Omar E. Pol, Nov 20 2016

Status

approved