A177404 Numbers n such that n^2 minus (sum of the squares of the proper divisors of n) is a prime number.

2, 4, 8, 9, 18, 25, 32, 49, 64, 72, 81, 100, 121, 162, 242, 256, 289, 361, 392, 400, 484, 512, 529, 576, 648, 729, 784, 1058, 1296, 1352, 1444, 1681, 1849, 1922, 2048, 2116, 2500, 3136, 3872, 4418, 4608, 4624, 5184, 5776, 5832, 6889, 7225, 7396, 7744

Offset: 1

Author

Claudio Meller, Dec 10 2010

Keywords

• nonn

Comments

Sum of squares of proper divisors of n is given by A067558.

Examples

			9 has proper divisors 3 and 1; it is in the list because 9^2-(3^2+1^2) = 71 is a prime number.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A067558.

Programs

Magma

a067558:=func< n | n le 1 select 0 else &+[ D[k]^2: k in [1..#D-1] ] where D is Divisors(n) >; [ n: n in [1..10000] | IsPrime(n^2-a067558(n)) ];

Mathematica

Select[Range[8000],PrimeQ[#^2-Total[Most[Divisors[#]]^2]]&] (* Harvey P. Dale, Dec 14 2011 *)