A125237 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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