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 A382926 #20 May 09 2025 00:55:23
%S A382926 2,3,4,5,3,4,6,7,8,9,4,5,8,10,11,6,8,9,12,13,4,7,8,14,5,9,15,16,17,8,
%T A382926 9,12,16,18,19,5,8,10,16,20,7,9,21,4,8,11,16,22,23,9,12,16,18,24,25,4,
%U A382926 8,13,16,26,27,7,8,14,16,28,29,8,9,10,12,15,16,18,20,24,25,27,30
%N A382926 Irregular table where row n lists numbers k in row n of A162306 for which there exists a prime p | n such that k*p > n.
%C A382926 The number n appears in each row. For n in A024619, for all p|n, p^floor(log_p n) is in row n. Thus, the number of terms in row n for n in A024619 is at least 1+omega(n), where omega = A001221 is the number of distinct prime factors of n.
%H A382926 Michael De Vlieger, <a href="/A382926/b382926.txt">Table of n, a(n) for n = 2..11938</a> (rows n = 2..1000, flattened)
%F A382926 For n in A000961, row n is {n}.
%e A382926 Let s(n) = A382964(n).
%e A382926 Table of select rows:
%e A382926 n s(n) row n of this sequence
%e A382926 --------------------------------------------------------
%e A382926 6 3 3, 4, 6;
%e A382926 10 4 4, 5, 8, 10;
%e A382926 12 4 6, 8, 9, 12;
%e A382926 14 4 4, 7, 8, 14;
%e A382926 15 3 5, 9, 15;
%e A382926 18 5 8, 9, 12, 16, 18;
%e A382926 20 5 5, 8, 10, 16, 20;
%e A382926 21 3 7, 9, 21;
%e A382926 22 5 4, 8, 11, 16, 22;
%e A382926 24 5 9, 12, 16, 18, 24;
%e A382926 26 5 4, 8, 13, 16, 26;
%e A382926 28 5 7, 8, 14, 16, 28;
%e A382926 30 12 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30.
%e A382926 In the examples below, we place terms in row n in brackets [] among other terms in row n of A162306, presented in order of row n of A275280.
%e A382926 Row p^m for m > 0 and prime p is {p^m}, since multiplying p^m by p exceeds p^m.
%e A382926 Row 10 = {4, 5, 8, 10}, since numbers k such that rad(k) | 10 contains these numbers, furthermore, we have the following: 2 or 5 times 8 exceeds 10, 5*4 > 10, 2 or 5 times 10 exceeds 10, and 5*5 > 10.
%e A382926 1 2 [4] [8]
%e A382926 [5] [10]
%e A382926 Row 24 = {9, 12, 16, 18, 24}, since numbers k such that rad(k) | 24 contains these numbers, furthermore, we have the following: 2 or 3 times 16 exceeds 24, 2 or 3 times 24 exceeds 24, 3*12 > 24, 2 or 3 times 18 exceeds 24, and 3*9 > 24.
%e A382926 1 2 4 8 [16]
%e A382926 3 6 [12] [24]
%e A382926 [9] [18]
%t A382926 (* First, run the "regs" function from A369609, then: *)
%t A382926 Table[Select[regs[n], Function[k, AnyTrue[FactorInteger[n][[All, 1]], #*k > n &]]], {n, 2, 30}] // Flatten
%Y A382926 Cf. A000961, A007947, A024619, A162306, A275280, A382964 (row lengths).
%K A382926 nonn,tabf
%O A382926 2,1
%A A382926 _Michael De Vlieger_, Apr 28 2025