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%I #11 Feb 06 2021 22:16:48
%S 42,54,66,78,102,114,135,138,147,156,162,174,186,192,222,228,246,250,
%T 258,282,318,354,366,372,402,426,438,444,474,498,507,516,534,582,606,
%U 618,642,654,678,686,732,762,786,804,822,834,845,876,894,906,942,948,978,1002,1029,1038,1074,1083,1086
%N Numbers k such that A341117(k) is divisible by k and k is not a prime or power of a prime.
%C If k is a prime or power of a prime, A341117(k) is divisible by k.
%C Contains no semiprimes.
%H Robert Israel, <a href="/A341129/b341129.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 66 is a term because 66 = 2*3*11 is not a prime or power of a prime and A341117(66) = 20262 = 66*307.
%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 -> not isprime(t) and nops(numtheory:-factorset(t))>1 and f(t) mod t = 0, [$2..10000]);
%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) = !(isprimepower(m) || (m==1)) && !(f(m) % m); \\ _Michel Marcus_, Feb 05 2021
%Y Cf. A341039, A341117.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Feb 05 2021
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