A244447 a(n) is the smallest integer m such that m-n is composite and phi(m+n) + sigma(m-n) = 2*m.

11, 8, 13, 37350, 25, 18, 28, 20, 61, 22, 44, 40, 52, 250, 39, 60, 68, 60, 58, 76, 168, 46, 92, 69, 2040, 56, 126, 84, 114, 140, 88, 74, 108, 90, 288, 92, 148, 108, 283, 324, 164, 180, 100, 40878, 125, 474, 162, 108, 773, 71, 111, 240, 168, 315, 148, 194, 564, 390, 128, 144, 124, 164, 153, 279, 1008, 162, 102, 152, 432, 222

Offset: 1

Author

Jahangeer Kholdi and Farideh Firoozbakht, Aug 30 2014

Keywords

• nonn

Comments

For each n, a(n)>n and like a(n)-n, a(n)+n is also composite.

If both numbers p and p+2n are primes then x=p+n is a solution to the equation phi(x+n)+sigma(x-n)=2x. But for these many solutions x, both numbers x-n and x+n are primes.

Examples

			a(1)=11 because 11-1 is composite, phi(11+1)+sigma(11-1)=2*11 and there is no such number less than 11.
		

Crossrefs

Cf. A000010, A000203, A244446, A244448.

Programs

Mathematica

a[n_]:=(For[m=n+1,PrimeQ[m-n]||EulerPhi[m+n]+DivisorSigma[1,m-n]!=2m,m++];m);Table[a[n],{n,70}]

PARI

a(n)=m=n+4;while(isprime(m-n)||eulerphi(m+n)+sigma(m-n)!=2*m,m++);m
vector(100,n,a(n)) \\ Derek Orr, Aug 30 2014