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A338930 Numbers k such that Sum_{d | k} (d^2 mod k) is prime. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Terms that are even are in A028982.
LINKS
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 16 2020
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)