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 A386807 #13 Aug 03 2025 16:05:35
%S A386807 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A386807 27,28,29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
%U A386807 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
%N A386807 Numbers without an exponent 5 in their prime factorization.
%C A386807 First differs from its subsequence A166718 at n = 47: a(47) = 48 = 2^4 * 3 is not a term of A166718.
%C A386807 Differs from A373868 by having the terms 1, 1024, 32768, 59049, ..., and not having the terms 96, 160, 224, ... .
%C A386807 These numbers were named semi-5-free integers by Suryanarayana (1971).
%C A386807 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^5 + 1/p^6) = 0.98136375107187963656... (Suryanarayana, 1971).
%H A386807 Amiram Eldar, <a href="/A386807/b386807.txt">Table of n, a(n) for n = 1..10000</a>
%H A386807 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 A386807 D. Suryanarayana, <a href="https://eudml.org/doc/141006">Semi-k-free integers</a>, Elemente der Mathematik, Vol. 26 (1971), pp. 39-40.
%H A386807 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 A386807 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%t A386807 Select[Range[100], !MemberQ[FactorInteger[#][[;; , 2]], 5] &]
%o A386807 (PARI) isok(k) = vecsum(apply(x -> if(x == 5, 1, 0), factor(k)[, 2])) == 0;
%Y A386807 A166718 is a subsequence.
%Y A386807 Cf. A373868.
%Y A386807 Numbers without an exponent k in their prime factorization: A001694 (k=1), A337050 (k=2), A386799 (k=3), A386803 (k=4), this sequence (k=5).
%Y A386807 Numbers that have exactly m exponents in their prime factorization that are equal to 5: this sequence (m=0), A386808 (m=1), A386809 (m=2), A386810 (m=3).
%K A386807 nonn,easy
%O A386807 1,2
%A A386807 _Amiram Eldar_, Aug 03 2025