A158914 Primes p such that there is a composite c with sigma_2(p)=sigma_2(c).

7, 47, 157, 3863

Offset: 1

Author

T. D. Noe, Mar 30 2009

Keywords

• more
• nonn

Comments

No other terms less than 10^8.

The corresponding composite numbers are 6, 40, 136, and 3352.

Is this sequence finite?

See A158913 for the sequence for sigma_1.

Terms 47, 157, 3863 are x values of solutions to Pell-Fermat equation x^2 - 85*y^2 = 84, where y is also prime and c = 8*y. For any other solution (x,y) formed by primes, x is a term. - Max Alekseyev, Jun 14 2025

Programs

Mathematica

tp=DivisorSigma[2,Select[Range[4000],PrimeQ]]; tc=DivisorSigma[2,Select[Range[4000],!PrimeQ[ # ]&]]; Sqrt[Intersection[tp,tc]-1]