This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A183098 #24 Sep 03 2023 10:42:54
%S A183098 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 A183098 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 A183098 71,93,53,83,71,107,79,89,59,163,61,95,94,2,83,143,67,121,95,143,71,65,73,113,98,135,95,167,79,157,3,125,83,219,107,131,119,167,89,224,111,163,127,143,119,191,97,121,146,87
%N A183098 a(1) = 0, a(n) = sum of divisors d of n such that if d = Product_{i} (p_i^e_i) then not all e_i are > 1.
%C A183098 a(n) = sum of non-powerful divisors d of n where powerful numbers are numbers from A001694(m) for m >= 2.
%C A183098 Sequence is not the same as A183101(n): a(72) = 65, A183101(72) = 137.
%H A183098 Antti Karttunen, <a href="/A183098/b183098.txt">Table of n, a(n) for n = 1..16385</a>
%H A183098 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A183098 a(n) = A000203(n) - A183097(n) = A183100(n) - 1.
%F A183098 a(1) = 0, a(p) = p, a(p*q) = p+q+p*q, a(p*q*...*z) = (p+1)*(q+1)*...*(z+1) - 1, a(p^k) = p, for p, q = primes, k = natural numbers, p*q*...*z = product of k (k > 2) distinct primes p, q, ..., z.
%e A183098 For n = 12, the set of such divisors is {2, 3, 6, 12}; a(12) = 2+3+6+12 = 23.
%t A183098 f1[p_, e_] := (p^(e+1)-1)/(p-1); f2[p_, e_] := f1[p, e] - p; a[1] = 0; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) - Times @@ f2 @@@ f; Array[a, 100] (* _Amiram Eldar_, Aug 29 2023 *)
%o A183098 (PARI) A183098(n) = sumdiv(n, d, d*(!ispowerful(d))); \\ _Antti Karttunen_, Oct 07 2017
%Y A183098 Cf. A000203, A001694, A183097, A183100, A183101, A183103.
%K A183098 nonn,easy
%O A183098 1,2
%A A183098 _Jaroslav Krizek_, Dec 25 2010
%E A183098 Name corrected by _Jon E. Schoenfield_, Aug 29 2023