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 A305056 #8 Jun 29 2019 11:35:35
%S A305056 1,1,2,1,2,4,6,8,2,4,6,8,12,24,4,6,8,12,24,48,72,120,12,24,48,72,120,
%T A305056 144,240,288,24,48,72,120,144,240,288,360,720,72,120,144,240,288,360,
%U A305056 720,72,1440,2160,120,144,240,288,360,720,1440,2160,2880,4320,5040
%N A305056 a(n) = A004394(n)/A002110(A001221(A004394(n))).
%C A305056 This sequence is analogous to A301413, which pertains to A002182.
%C A305056 Since A002182(20) = 7560 is not in A004394, a(20) =/= A301413(20), i.e., the former is 36, the latter 48. (The number 36 is not in this sequence, but is in A301413.)
%C A305056 A004394(50) = 120*A002110(8) is the smallest number in A004394 but not in A002182; in A004394 we have 120*A002110(m) for 4 <= m <= 8, while in A002110 we have 120*A002110(m) for 4 <= m <= 7. Therefore this sequence has one more instance of 120 (= a(50)) than exists in A301413.
%H A305056 Amiram Eldar, <a href="/A305056/b305056.txt">Table of n, a(n) for n = 1..1000</a>
%e A305056 Let m be a value in this sequence. The table below shows m*A002110(A001221(A004394(k))). Columns are A001221(A004394(k)), rows are m whose products m*A002110(A001221(A004394(k))) appear in A004394 are in this sequence. Numbers in A004394 that also appear in A004490 are followed by (*).
%e A305056 0 1 2 3 4 5 6 ...
%e A305056 +----------------------------------------------------
%e A305056 1 | 1 2* 6*
%e A305056 2 | 4 12* 60*
%e A305056 4 | 24 120* 840
%e A305056 6 | 36 180 1260
%e A305056 8 | 48 240 1680
%e A305056 12 | 360* 2520* 27720
%e A305056 24 | 720 5040* 55440* 720720*
%e A305056 Up to this point, the graph of this sequence and that of A301413 are identical; the asterisks pertain to numbers in A002201 in the case of A301413, but all the numbers on the graph are found in both A004490 and A002201, i.e., in A224078. The next two rows of the graph of A301413:
%e A305056 0 1 2 3 4 5 6 ...
%e A305056 +----------------------------------------------------
%e A305056 36 | 7560 83160 1081080
%e A305056 48 | 10080 110880 1441440*
%e A305056 ...
%e A305056 but this sequence does not have row m = 36, as {7560, 83160, 1081080} are not in A004394.
%t A305056 Block[{s = Array[DivisorSigma[1, #]/# &, 10^6], t}, t = Union@ FoldList[Max, s]; Map[#/Product[Prime@ i, {i, PrimeNu@ #}] &@ First@ FirstPosition[s, #] &, t]]
%Y A305056 Cf. A001221, A002110, A004394, A301413.
%K A305056 nonn
%O A305056 1,3
%A A305056 _Michael De Vlieger_, Jul 01 2018