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 A386799 #14 Aug 03 2025 10:21:07
%S A386799 1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,28,
%T A386799 29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,
%U A386799 53,55,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74,75
%N A386799 Numbers without an exponent 3 in their prime factorization.
%C A386799 First differs from its subsequence A336592 at n = 116: a(116) = 128 = 2^7 is not a term of A336592.
%C A386799 Numbers k such that A295883(k) = 0.
%C A386799 These numbers were named semi-3-free integers by Suryanarayana (1971).
%C A386799 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^3 + 1/p^4) = 0.90470892696874750603... (Suryanarayana, 1971).
%H A386799 Amiram Eldar, <a href="/A386799/b386799.txt">Table of n, a(n) for n = 1..10000</a>
%H A386799 Ertan Elma and Greg Martin, <a href="https://doi.org/10.4153/S0008439524000584">Distribution of the number of prime factors with a given multiplicity</a>, Canadian Mathematical Bulletin, Vol. 67, No. 4 (2024), pp. 1107-1122; <a href="https://arxiv.org/abs/2406.04574">arXiv preprint</a>, arXiv:2406.04574 [math.NT], 2024.
%H A386799 D. Suryanarayana, <a href="https://eudml.org/doc/141006">Semi-k-free integers</a>, Elemente der Mathematik, Vol. 26 (1971), pp. 39-40.
%H A386799 D. Suryanarayana and R. Sitaramachandra Rao, <a href="https://doi.org/10.1090/S0002-9939-1973-0311599-1">Distribution of semi-k-free integers</a>, Proceedings of the American Mathematical Society, Vol. 37, No. 2 (1973), pp. 340-346.
%H A386799 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%t A386799 Select[Range[100], !MemberQ[FactorInteger[#][[;; , 2]], 3] &]
%o A386799 (PARI) isok(k) = vecsum(apply(x -> if(x == 3, 1, 0), factor(k)[, 2])) == 0;
%Y A386799 Complement of A176297.
%Y A386799 A336592 is a subsequence.
%Y A386799 Cf. A295883.
%Y A386799 Numbers without an exponent k in their prime factorization: A001694 (k=1), A337050 (k=2), this sequence (k=3), A386803 (k=4), A386807 (k=5).
%Y A386799 Numbers that have exactly m exponents in their prime factorization that are equal to 3: this sequence (m=0), A386800 (m=1), A386801 (m=2), A386802 (m=3).
%K A386799 nonn,easy
%O A386799 1,2
%A A386799 _Amiram Eldar_, Aug 02 2025