A092590 a(n) = A065395(A000040(n)); values of commutator of sigma and phi function at prime number arguments.

-1, 1, 5, 8, 14, 22, 25, 31, 28, 48, 56, 73, 78, 76, 56, 80, 74, 138, 112, 120, 159, 136, 102, 156, 210, 185, 168, 126, 240, 212, 248, 212, 226, 240, 226, 300, 314, 283, 204, 252, 222, 474, 296, 412, 339, 388, 472, 360, 270, 472, 378, 368, 634, 396, 427, 316, 404, 592, 534, 628, 436, 434, 582, 480, 684, 456, 700, 836

Offset: 1

Author

Labos Elemer, Mar 03 2004

Keywords

• sign
• look

Comments

The sequence differs from A065394 since it is not monotonic.

Examples

			a(1) = sigma(phi(2))- phi(sigma(2)) = sigma(1)-phi(3) = 1-2 = -1.
		

Links

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

Crossrefs

Cf. A000010, A000040, A000203, A033632, A065393, A065394, A065395, A008331, A008332, A092584, A092585, A092586, A092587, A092588, A092589.

Programs

Magma

[DivisorSigma(1,EulerPhi(p))-EulerPhi(DivisorSigma(1,p)): p in PrimesUpTo(400)]; // Bruno Berselli, Oct 20 2015

Mathematica

Table[DivisorSigma[1, p-1] - EulerPhi[p+1], {p, Prime[Range[100]]}] (* Amiram Eldar, Jun 09 2024 *)

Formula

a(n) = sigma(prime(n)-1) - phi(prime(n)+1) = A008332(n) - A008331(n). - Amiram Eldar, Jun 09 2024