A091554 Primes p such that k = 2p is the smallest positive solution to the equation sigma(p+k) = sigma(p) + sigma(k).

7, 11, 13, 17, 19, 23, 31, 53, 59, 73, 79, 89, 97, 103, 109, 113, 137, 139, 149, 157, 163, 181, 193, 211, 223, 227, 269, 281, 293, 313, 331, 337, 373, 389, 397, 409, 419, 421, 433, 463, 467, 487, 499, 509, 521, 523, 541, 547, 571, 599, 601, 617, 631, 641, 643

Offset: 1

Author

T. D. Noe, Jan 20 2004

Keywords

• nonn

Comments

Note that for all primes p > 3, sigma(3p) = sigma(p) + sigma(2p).

Crossrefs

Cf. A066435 (least k such that sigma(n+k)=sigma(n)+sigma(k)).

Programs

Mathematica

lst={}; Do[p=Prime[n]; k=1; While[DivisorSigma[1, p+k]!=DivisorSigma[1, p]+DivisorSigma[1, k], k++ ]; If[k==2p, AppendTo[lst, p]], {n, 3, 200}]; lst