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%I #14 Feb 07 2021 19:38:55
%S 84,154,364,390,418,420,440,510,760,870,874,900,966,1102,1144,1330,
%T 1380,1406,1428,1575,1610,1624,1674,1702,1736,1776,1886,1890,1924,
%U 1998,2030,2052,2146,2220,2256,2320,2322,2378,2542,2584,2666,2800,2862,3034,3074,3132,3168,3192,3224,3248,3286,3344
%N Numbers k such that A341117(k) is prime.
%C Contains no prime powers or semiprimes.
%H Robert Israel, <a href="/A341128/b341128.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 364 is a term because A341117(364) = 609149 is prime.
%p f:= proc(n) local D, S,i;
%p D:= sort(convert(numtheory:-divisors(n),list),`>`);
%p S:= ListTools:-PartialSums(D);
%p add(D[i]*S[-i],i=1..nops(D))
%p end proc:
%p select(t -> isprime(f(t)), [$1..4000]);
%t 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 *)
%o (PARI) f(n) = my(d=divisors(n)); sum(k=1, #d, d[k]*sum(i=#d-k+1, #d, d[i])); \\ A341117
%o isok(m) = isprime(f(m)); \\ _Michel Marcus_, Feb 05 2021
%Y Cf. A341117.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Feb 05 2021
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