A338930 Numbers k such that Sum_{d | k} (d^2 mod k) is prime.

8, 16, 18, 21, 39, 45, 55, 57, 93, 98, 99, 100, 111, 119, 129, 144, 153, 162, 183, 203, 205, 219, 231, 237, 245, 261, 273, 291, 309, 341, 355, 377, 381, 413, 417, 429, 471, 481, 484, 489, 505, 511, 513, 517, 543, 583, 603, 609, 629, 637, 639, 651, 655, 669, 676, 687, 689, 697, 707, 722, 723, 731

Offset: 1

Author

J. M. Bergot and Robert Israel, Nov 16 2020

Keywords

• nonn

Comments

Terms that are even are in A028982.

Examples

			a(3) = 18 is in the sequence because Sum_{d|18} (d^2 mod 18) =  (1^2 mod 18) + (2^2 mod 18) + (3^2 mod 18) + (6^2 mod 18) + (9^2 mod 18) + (18^2 mod 18) = 1 + 4 + 9 + 0 + 9 + 0 = 23 is prime.
		

Links

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

Crossrefs

Cf. A028982.

Programs

Maple

filter:= proc(n) local t;
  isprime(add(t^2 mod n, t = numtheory:-divisors(n)))
end proc:
select(filter, [$1..1000]);

Mathematica

Select[Range[800],PrimeQ[Total[PowerMod[Divisors[#],2,#]]]&] (* Harvey P. Dale, Dec 31 2021 *)

PARI

isok(m) = isprime(sumdiv(m, d, lift(Mod(d, m)^2))); \\ Michel Marcus, Nov 16 2020