login
A341128
Numbers k such that A341117(k) is prime.
1
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
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 05 2021
STATUS
approved