A341128 Numbers k such that A341117(k) is prime.

84, 154, 364, 390, 418, 420, 440, 510, 760, 870, 874, 900, 966, 1102, 1144, 1330, 1380, 1406, 1428, 1575, 1610, 1624, 1674, 1702, 1736, 1776, 1886, 1890, 1924, 1998, 2030, 2052, 2146, 2220, 2256, 2320, 2322, 2378, 2542, 2584, 2666, 2800, 2862, 3034, 3074, 3132, 3168, 3192, 3224, 3248, 3286, 3344

Offset

1,1

Comments

Contains no prime powers or semiprimes.

Links

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

Example

a(3) = 364 is a term because A341117(364) = 609149 is prime.

Maple

f:= proc(n) local D, S, i;
  D:= sort(convert(numtheory:-divisors(n), list), `>`);
  S:= ListTools:-PartialSums(D);
  add(D[i]*S[-i], i=1..nops(D))
end proc:
select(t -> isprime(f(t)), [$1..4000]);

Mathematica

Position[Array[Sum[#1[[k]]*Sum[#1[[j]], {j, #2 - k + 1, #2}], {k, #2}] & @@ {Divisors[#], DivisorSigma[0, #]} &, 3400], _?PrimeQ][[All, 1]] (* Michael De Vlieger, Feb 05 2021 *)

Prog

(PARI) f(n) = my(d=divisors(n)); sum(k=1, #d, d[k]*sum(i=#d-k+1, #d, d[i])); \\ A341117
isok(m) = isprime(f(m)); \\ Michel Marcus, Feb 05 2021

Crossrefs

Cf. A341117.

Sequence in context: A101260 A141502 A039499 * A055712 A066292 A260703

Adjacent sequences: A341125 A341126 A341127 * A341129 A341130 A341131

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 05 2021

Status

approved