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 A183095 #20 Jan 30 2025 08:22:56
%S A183095 1,2,2,2,2,4,2,2,2,4,2,5,2,4,4,2,2,5,2,5,4,4,2,6,2,4,2,5,2,8,2,2,4,4,
%T A183095 4,6,2,4,4,6,2,8,2,5,5,4,2,7,2,5,4,5,2,6,4,6,4,4,2,11,2,4,5,2,4,8,2,5,
%U A183095 4,8,2,7,2,4,5,5,4,8,2,7,2,4,2,11,4,4,4,6,2,11,4,5,4,4,4,8,2,5,5,6
%N A183095 a(n) = number of divisors d of n that are either 1 or of the form Product_(i) (p_i^e_i) where e_i = 1 for at least one i.
%C A183095 a(n) = number of non-powerful divisors d of n where powerful numbers are numbers of the form A001694(m) for m >= 1.
%H A183095 Antti Karttunen, <a href="/A183095/b183095.txt">Table of n, a(n) for n = 1..10000</a>
%H A183095 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A183095 a(n) = A000005(n) - A183094(n) = A183093(n) + 1.
%F A183095 a(1) = 1, a(p) = 2, a(pq) = 4, a(pq...z) = 2^k, a(p^k) = 2, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.
%F A183095 Sum_{k=1..n} a(k) ~ n*(log(n) + 2*gamma - zeta(2)*zeta(3)/zeta(6)), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Jan 30 2025
%e A183095 For n = 12, set of such divisors is {1, 2, 3, 6, 12}; a(12) = 5.
%t A183095 nonpowQ[n_] := Min[FactorInteger[n][[;;, 2]]] == 1;a[n_] := DivisorSum[n, 1 &, nonpowQ[#] &]; Array[a, 100] (* _Amiram Eldar_, Jan 30 2025 *)
%o A183095 (PARI) a(n) = sumdiv(n, d, d == 1 || vecmin(factor(d)[, 2]) == 1); \\ _Amiram Eldar_, Jan 30 2025
%Y A183095 Cf. A000005, A001694, A183093, A183094.
%Y A183095 Cf. A001620, A082695.
%K A183095 nonn
%O A183095 1,2
%A A183095 _Jaroslav Krizek_, Dec 25 2010
%E A183095 Name corrected by _Amiram Eldar_, Jan 30 2025