

A253473


a(n) = phi(c(n))  tau(phi(c(n))), where c(n) is the nth composite number.


2



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
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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



