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%I #15 May 30 2021 11:25:54
%S 0,2,3,2,5,11,7,2,3,17,11,23,13,23,23,2,17,29,19,37,31,35,23,47,5,41,
%T 3,51,29,71,31,2,47,53,47,41,37,59,55,77,41,95,43,79,68,71,47,95,7,67,
%U 71,93,53,83,71,107,79,89,59,163,61,95,94,2,83,143,67,121,95,143,71,137,73,113,98,135,95,167,79,157,3,125,83,219,107,131,119,167,89,224,111,163,127,143,119,191,97,121,146,87
%N a(n) = sum of divisors of n that are not perfect powers.
%C Sequence is not the same as A183098(n): a(72) = 137, A183098(72) = 65.
%H Antti Karttunen, <a href="/A183101/b183101.txt">Table of n, a(n) for n = 1..16385</a>
%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F a(n) = A000203(n) - A091051(n).
%F a(1) = 0, a(p) = p, a(pq) = p+q+pq, a(pq...z) = [(p+1)*(q+1)*…*(z+1)]-1, a(p^k) = p, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.
%e For n = 12, set of such divisors is {2, 3, 6, 12}; a(12) = 2+3+6+12=23.
%p N:= 1000: # to get a(1) to a(N)
%p S:= {seq(seq(i^k, i=1..floor(N^(1/k))), k=2..ilog2(N))}:
%p seq(convert(numtheory:-divisors(t) minus S,`+`), t=1..N); # _Robert Israel_, Oct 02 2014
%t Table[Total[DeleteCases[Divisors[n],_?(GCD@@FactorInteger[#][[All,2]]>1&)]],{n,100}]-1 (* _Harvey P. Dale_, May 30 2021 *)
%o (PARI) a(n) = sumdiv(n, d, d*((d!=1) && !ispower(d))); \\ _Michel Marcus_, Oct 02 2014
%Y Cf. A000203, A091051, A183098, A183105.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Dec 25 2010
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