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 A386803 #12 Aug 04 2025 01:09:59
%S A386803 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,
%T A386803 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,
%U A386803 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70
%N A386803 Numbers without an exponent 4 in their prime factorization.
%C A386803 First differs from its subsequence A209061 at n = 246: a(246) = 256 = 2^8 is not a term of A209061.
%C A386803 First differs from its subsequences A115063 and A369939 at n = 62: a(62) = 64 = 2^6 is not a term of A115063.
%C A386803 The complement of this sequence is a subsequence of A336595.
%C A386803 These numbers were named semi-4-free integers by Suryanarayana (1971).
%C A386803 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^4 + 1/p^5) = 0.95908865419555719109... (Suryanarayana, 1971).
%H A386803 Amiram Eldar, <a href="/A386803/b386803.txt">Table of n, a(n) for n = 1..10000</a>
%H A386803 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 A386803 D. Suryanarayana, <a href="https://eudml.org/doc/141006">Semi-k-free integers</a>, Elemente der Mathematik, Vol. 26 (1971), pp. 39-40.
%H A386803 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 A386803 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%t A386803 Select[Range[100], !MemberQ[FactorInteger[#][[;; , 2]], 4] &]
%o A386803 (PARI) isok(k) = vecsum(apply(x -> if(x == 4, 1, 0), factor(k)[, 2])) == 0;
%Y A386803 Subsequences: A115063, A209061, A369939.
%Y A386803 Numbers without an exponent k in their prime factorization: A001694 (k=1), A337050 (k=2), A386799 (k=3), this sequence (k=4), A386807 (k=5).
%Y A386803 Numbers that have exactly m exponents in their prime factorization that are equal to 4: this sequence (m=0), A386804 (m=1), A386805 (m=2), A386806 (m=3).
%K A386803 nonn,easy
%O A386803 1,2
%A A386803 _Amiram Eldar_, Aug 03 2025