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 A371630 #30 Jun 14 2024 11:34:23
%S A371630 1,2,6,12,30,60,120,210,420,840,1260,1680,2520,4620,9240,13860,18480,
%T A371630 27720,32760,55440,65520,102960,110880,120120,180180,240240,360360,
%U A371630 556920,720720,1081080,1441440,1884960,2162160,2827440,2882880,3063060,3603600,4084080,6126120
%N A371630 Numbers k that set records in A372720.
%C A371630 In other words, numbers k that set records for d(k) - f(k), where d = A000005 and f = A008479.
%C A371630 Largest primorial in this sequence is A002110(4) = 210.
%C A371630 The primorials A002110(0..4) are the only squarefree numbers in this sequence.
%C A371630 {a(n)} \ A002110(0..4) is contained in A126706.
%C A371630 Not a subset of A060735; a(13) = 2520 is not in A060735. Though common for small n, the set of a(n) in A060735 is likely finite; the restriction is connected with the finite number of primorials in the sequence.
%C A371630 Not a subset of A025487 or A055932; a(19) = 32760 is the smallest term without a primorial kernel.
%C A371630 The prime shape of a(n) appears to feature exponents m of prime power factors p^m | a(n) that are nonincreasing as pi(p) increases.
%H A371630 Michael S. Branicky, <a href="/A371630/b371630.txt">Table of n, a(n) for n = 1..67</a> (terms 1..56 from Michael De Vlieger)
%H A371630 Michael De Vlieger, <a href="/A371630/a371630.txt">Prime power decomposition of A371630(n)</a>, n = 1..56.
%e A371630 Table of a(n) and A371634(n) = b(n) for n = 1..20. Asterisks in the a(n) column denote squarefree terms while "+" denotes numbers not in A055932 (i.e., in A080259).
%e A371630 n a(n) A067255(a(n)) d(n)-f(n) = b(n)
%e A371630 ------------------------------------------------------
%e A371630 1 1* 1 1 - 1 = 0
%e A371630 2 2* 2 2 - 1 = 1
%e A371630 3 6* 2 * 3 4 - 1 = 3
%e A371630 4 12 2^2 * 3 6 - 2 = 4
%e A371630 5 30* 2 * 3 * 5 8 - 1 = 7
%e A371630 6 60 2^2 * 3 * 5 12 - 2 = 10
%e A371630 7 120 2^3 * 3 * 5 16 - 4 = 12
%e A371630 8 210* 2 * 3 * 5 * 7 16 - 1 = 15
%e A371630 9 420 2^2 * 3 * 5 * 7 24 - 2 = 22
%e A371630 10 840 2^3 * 3 * 5 * 7 32 - 4 = 28
%e A371630 11 1260 2^2 * 3^2 * 5 * 7 36 - 6 = 30
%e A371630 12 1680 2^4 * 3 * 5 * 7 40 - 8 = 32
%e A371630 13 2520 2^3 * 3^2 * 5 * 7 48 - 11 = 37
%e A371630 14 4620 2^2 * 3 * 5 * 7 * 11 48 - 2 = 46
%e A371630 15 9240 2^3 * 3 * 5 * 7 * 11 64 - 4 = 60
%e A371630 16 13860 2^2 * 3^2 * 5 * 7 * 11 72 - 6 = 66
%e A371630 17 18480 2^4 * 3 * 5 * 7 * 11 80 - 8 = 72
%e A371630 18 27720 2^3 * 3^2 * 5 * 7 * 11 96 - 12 = 84
%e A371630 19 32760+ 2^3 * 3^2 * 5 * 7 * 13 96 - 11 = 85
%e A371630 20 55440 2^4 * 3^2 * 5 * 7 * 11 120 - 20 = 100
%Y A371630 Cf. A000005, A002110, A008479, A055932, A060735, A080259, A126706, A371634, A372720.
%K A371630 nonn,hard
%O A371630 1,2
%A A371630 _Michael De Vlieger_, Jun 04 2024