A125249 Numbers n for which the absolute values of the abundances of n, n^2 and n^3 are all prime numbers.
289, 201601, 222784, 638401, 868562, 910116, 4694048, 4950625, 8994001, 9054081, 19855936, 30085225, 32385152, 47623801, 55100929, 72182016, 78952178, 85099058, 86303522, 91910569, 104040000, 105678400, 111175936, 112530002, 128504896, 133702969, 193043236, 204404209, 216001809, 237961476
Offset: 1
Keywords
Examples
n=289; The abundance of 289 is -271, the abundance of 83521 (289^2) is -78301, the abundance of 24137569 (289^3) is -22628971 - all of which are negatives of primes.
Programs
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PARI
{for(n=1,1000000,if(isprime(abs(sigma(n)-2*n))&&isprime(abs(sigma(n^2)-2*n^2))&&isprime(abs(sigma(n^3)-2*n^3)),print1(n,",")))}
Extensions
More terms from Stefan Steinerberger, May 29 2007
a(21)-a(24) from Donovan Johnson, Feb 19 2009
a(25)-a(30) from Jason G. Wurtzel, Sep 24 2014