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

1,1

Comments

Terms that are even are in A028982.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A028982.

Sequence in context: A356450 A328189 A101766 * A357002 A356441 A140270

Adjacent sequences: A338927 A338928 A338929 * A338931 A338932 A338933

Keyword

nonn

Author

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

Status

approved