A085122 -id:A085122 - cp's OEIS frontend

A085343 Number of primes between sigma(n) and phi(n) inclusive.

0, 2, 1, 3, 1, 4, 1, 4, 3, 5, 1, 7, 1, 6, 5, 7, 1, 9, 1, 9, 6, 7, 1, 13, 3, 8, 5, 11, 1, 16, 1, 12, 7, 10, 6, 19, 1, 10, 7, 18, 1, 19, 1, 15, 12, 12, 1, 24, 3, 16, 9, 16, 1, 23, 8, 21, 11, 15, 1, 33, 1, 14, 16, 20, 8, 26, 1, 19, 10, 25, 1, 35, 1, 19, 18, 23, 7, 30, 1, 31, 14, 18, 1, 39, 10, 19

Offset: 1

Labos Elemer, Jul 10 2003

nonn

a(p) = 1 for prime p > 2. Since phi(p) = p - 1 and sigma(p) = p + 1, the largest prime q < p - 1 must be the prime previous to p, while p itself is the largest prime less than p + 1 for p > 2. - Michael De Vlieger, Jan 22 2020

			n=12: sigma(12)=28, phi(n)=4, Pi(28)-Pi(4)=9-2=7.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000720, A000010, A000203, A070803, A070804, A085122, A085341-A085347.

Array[Subtract @@ PrimePi@{DivisorSigma[1, #], EulerPhi@ #} &, 86] (* Michael De Vlieger, Jan 22 2020 *)

a(n) = primepi(sigma(n)) - primepi(eulerphi(n)); \\ Michel Marcus, Aug 29 2019

a(n) = pi(sigma(n)) - pi(phi(n)) = A000720(A000203(n)) - A000720(A000010(n)).

a(n) = A070803(n) - A070804(n). - Antti Karttunen, Jan 22 2020

cp's OEIS Frontend

A085343 Number of primes between sigma(n) and phi(n) inclusive.

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