A070802 a(n)=prevprime[sigma(n)]-nextprime[phi(n)]=A070801(n)-A070800(n).

1, 0, 4, 0, 8, 0, 8, 6, 12, 0, 18, 0, 16, 12, 20, 0, 30, 0, 30, 18, 20, 0, 48, 8, 28, 18, 40, 0, 60, 0, 44, 24, 36, 18, 76, 0, 40, 24, 72, 0, 76, 0, 60, 44, 48, 0, 96, 10, 66, 34, 68, 0, 94, 30, 84, 42, 60, 0, 150, 0, 58, 66, 90, 30, 116, 0, 76, 42, 110, 0, 164, 0, 76, 72, 102, 28

Offset: 2

Author

Labos Elemer, May 08 2002

Keywords

• easy
• nonn

Examples

			n=100:sigma[100]=217,prevprime[217]=211, phi[100]=40,nextprime[40]=41,a(100)=211-41=170. The difference is 0 for odd primes.
		

Crossrefs

Cf. A007917, A007818, A000010, A000203, A000720, A000040, A070800, A070801.

Programs

Mathematica

Table[Prime[PrimePi[DivisorSigma[1, w]]]- Prime[1+PrimePi[EulerPhi[w]]], {w, 2, 128}]

Formula

a(n)=p[Pi(sigma[n])]-p[1+Pi(phi[n])]