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 A380694 #7 Jan 31 2025 04:24:21
%S A380694 3,5,7,11,13,15,17,19,21,23,25,29,31,33,35,37,39,41,43,47,49,51,53,55,
%T A380694 57,59,61,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,101,103,105,
%U A380694 107,109,111,113,115,119,121,123,127,129,131,133,137,139,141,143,145,149
%N A380694 Numbers k such that the prime index of the least prime dividing k is larger than the maximum exponent in the prime factorization of k.
%C A380694 Differs from A352830 by having the terms 1225, 13475, 15925, ... and not having the terms 1, 147, 363, 507, 867, 1083, ... .
%C A380694 Differs from A320055 by having the terms 105, 165, 195, ... and not having the terms 1 and 2.
%C A380694 Differs from A320056 by having the terms 105, 165, 195, ... and not having the term 1.
%C A380694 Numbers k such that A055396(k) > A051903(k).
%C A380694 Disjoint union of the sequences S_k, k >= 1, where S_k is the sequence of p-rough numbers (numbers whose prime factors are all greater than or equal to p), with p = prime(k+1), whose maximum exponent in their prime factorization is k (i.e., numbers that are (k+1)-free but not k-free, where k-free numbers are numbers whose prime factorization exponents do not exceed k).
%C A380694 The asymptotic density of this sequence is Sum_{i>=1} d(i) = 0.43156823896267860476......, where d(i), the density of S_i, equals f(i+1) * Product_{primes p <= prime(i)} ((1-1/p)/(1-1/p^(i+1))) - f(i) * Product_{primes p <= prime(i)} ((1-1/p)/(1-1/p^i)), f(i) = 1/zeta(i) if i >= 2, and f(1) = 0.
%H A380694 Amiram Eldar, <a href="/A380694/b380694.txt">Table of n, a(n) for n = 1..10000</a>
%H A380694 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RoughNumber.html">Rough Number</a>.
%H A380694 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rough_number">Rough number</a>.
%e A380694 3 = 3^1 is a term since PrimePi(3) = 2 > 1.
%e A380694 9 = 3^2 is not a term since PrimePi(3) = 2 is not larger than the exponent 2.
%e A380694 25 = 5^2 is a term since PrimePi(5) = 3 > 2.
%t A380694 q[k_] := k > 1 && Module[{f = FactorInteger[k]}, f[[1, 1]] > Prime[Max[f[[;; , 2]]]]]; Select[Range[150], q]
%o A380694 (PARI) isok(k) = if(k == 1, 0, my(f = factor(k), e = f[,2]); f[1,1] > prime(vecmax(e)));
%Y A380694 Cf. A000720, A020639, A051903, A055396.
%Y A380694 Cf. A352830, A320055, A320056.
%Y A380694 Subsequence of A380692, A380693 and A380695.
%K A380694 nonn,easy
%O A380694 1,1
%A A380694 _Amiram Eldar_, Jan 30 2025