A380520 Numbers m such that the sum of squares of nondivisors of m is prime.

5, 6, 26, 38, 66, 166, 206, 238, 266, 318, 321, 333, 341, 369, 405, 406, 445, 458, 481, 553, 606, 658, 706, 784, 873, 893, 933, 946, 1125, 1166, 1173, 1273, 1286, 1293, 1353, 1546, 1578, 1606, 1666, 1678, 1705, 1726, 1745, 1773, 1781, 1786, 1858, 1906, 1918, 1941

Offset: 1

Author

Michel Lagneau, Jan 26 2025

Keywords

• nonn

Examples

			Nondivisors of 6 are {4, 5} and their sum of squares 4^2 + 5^2 = 41 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024816, A200981, A380569.

Programs

Maple

filter:= proc(n) local d;
      isprime(n*(n+1)*(2*n+1)/6 - add(d^2,d=numtheory:-divisors(n)))
end proc:
select(filter, [$1..2000]); # Robert Israel, Feb 26 2025

Mathematica

Q1[n_]:=(n > 0) && PrimeQ[n]; Select[Range[2000], Q1[#(#+1)(2#+1)/6 - DivisorSigma[2, #]] &]

PARI

isok(k) = isprime(norml2(setminus([1..k], divisors(k)))); \\ Michel Marcus, Jan 28 2025