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

1,1

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A088005, A125236.

Sequence in context: A134073 A088005 A340459 * A085459 A092169 A093108

Adjacent sequences: A125234 A125235 A125236 * A125238 A125239 A125240

Keyword

nonn

Author

Jason G. Wurtzel, Nov 25 2006

Extensions

More terms from Klaus Brockhaus, Nov 25 2006

Status

approved