A077088 a(n) = phi(sigma(n) - phi(n)), where phi is Euler's totient function and sigma is the sum of divisors function, with a(1) = 0.

0, 1, 1, 4, 1, 4, 1, 10, 6, 6, 1, 8, 1, 6, 8, 22, 1, 20, 1, 16, 8, 12, 1, 24, 10, 8, 10, 20, 1, 32, 1, 46, 12, 18, 8, 78, 1, 12, 16, 36, 1, 24, 1, 32, 18, 20, 1, 36, 8, 72, 16, 36, 1, 32, 16, 32, 20, 30, 1, 72, 1, 20, 32, 72, 12, 60, 1, 46, 24, 32, 1, 108, 1, 24, 24, 48, 12, 48, 1, 60

Offset: 1

Author

Labos Elemer, Nov 04 2002

Keywords

• nonn
• easy

Comments

a(p) = 1 for p prime. Otherwise a(n) is even.

Examples

			a(10) = 6 because sigma(10) = 18 and phi(10) = 4, and so phi(18 - 4) = phi(14) = 6.
a(11) = 1 because sigma(11) = 12 and phi(11) = 10, so phi(12 - 10) = phi(2) = 1.
a(12) = 8 because sigma(12) = 28 and phi(12) = 4, so phi(28 - 4) = phi(24) = 8.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A000203, A051612, A065387. See iterations in A077090-A077100.

Programs

GAP

List([1..100],n->Phi(Sigma(n)-Phi(n))); # Muniru A Asiru, Mar 04 2018

Maple

with(numtheory); A077088:=n->phi(sigma(n)-phi(n)); seq(A077088(n), n=1..100); # Wesley Ivan Hurt, Dec 02 2013

Mathematica

Table[EulerPhi[DivisorSigma[1, n] - EulerPhi[n]], {n, 100}] (* Alonso del Arte, Nov 29 2013 *)

PARI

A077088(n) = if(1==n,0,eulerphi(sigma(n) - eulerphi(n))); \\ Antti Karttunen, Mar 04 2018

Formula

a(1) = 0; and for n > 1, a(n) = A000010(A051612(n)).

Extensions

Value of a(1) clarified by Antti Karttunen, Mar 04 2018