A244446 a(n) is the smallest integer m such that m-n is composite and phi(m-n) + sigma(m+n) = 2*m.

25, 323, 48, 34, 53, 471, 58, 78, 84, 76, 71, 122, 64, 144, 162, 118, 74, 188, 106, 258, 156, 2512, 68, 254, 94, 107, 132, 2326, 876, 536, 154, 182, 268, 468, 98, 2061, 106, 408, 264, 286, 258, 1520900, 423, 618, 276, 648, 579, 518, 204, 708, 196, 370, 164, 1088, 300, 1518, 412, 3616, 158, 1226

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

Examples

			a(1)=25 because 25-1 is composite, phi(25-1)+sigma(25+1)=2*25 and there is no such number less than 25.
		

Crossrefs

Cf. A000010, A000203, A244447, 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,60}]

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