A125237 Numbers n for which the absolute value of the abundance of both n and n^2 is a prime number.

3, 9, 10, 18, 50, 100, 104, 121, 136, 289, 464, 576, 650, 900, 5041, 6962, 7225, 10201, 14400, 55225, 65025, 87025, 102152, 147456, 171698, 174050, 179776, 182329, 189225, 201601, 222784, 291848, 312481, 380689, 410881, 469225, 481636, 488601

Offset: 1

Author

Jason G. Wurtzel, Nov 25 2006

Keywords

• nonn

Examples

			n=3: The abundance of 3 is -2, the negative of a prime. n^2=9, the abundance of 9 is -5, the negative of a prime as well.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A088005, A125236.

Programs

Mathematica

pQ[n_] := PrimeQ[DivisorSigma[1, n] - 2n]; Select[Range[10^4], pQ[#] && pQ[#^2] &] (* Amiram Eldar, Sep 24 2019 *)

PARI

{for(n=1, 500000, if(isprime(abs(sigma(n)-2*n)) && isprime(abs(sigma(n^2)-2*n^2)), print1(n, ",")))} \\ Klaus Brockhaus, Nov 25 2006

Extensions

More terms from Klaus Brockhaus, Nov 25 2006