A305056 a(n) = A004394(n)/A002110(A001221(A004394(n))).

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, 144, 240, 288, 24, 48, 72, 120, 144, 240, 288, 360, 720, 72, 120, 144, 240, 288, 360, 720, 72, 1440, 2160, 120, 144, 240, 288, 360, 720, 1440, 2160, 2880, 4320, 5040

Offset: 1

Author

Michael De Vlieger, Jul 01 2018

Keywords

• nonn

Comments

This sequence is analogous to A301413, which pertains to A002182.

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.)

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.

Examples

			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 (*).
         0     1     2      3      4       5         6  ...
      +----------------------------------------------------
   1  |  1     2*    6*
   2  |        4    12*    60*
   4  |             24    120*   840
   6  |             36    180   1260
   8  |             48    240   1680
  12  |                   360*  2520*  27720
  24  |                   720   5040*  55440*   720720*
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:
       0     1     2      3      4       5         6  ...
      +----------------------------------------------------
  36  |                         7560   83160   1081080
  48  |                        10080  110880   1441440*
  ...
but this sequence does not have row m = 36, as {7560, 83160, 1081080} are not in A004394.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A002110, A004394, A301413.

Programs

Mathematica

Block[{s = Array[DivisorSigma[1, #]/# &, 10^6], t}, t = Union@ FoldList[Max, s]; Map[#/Product[Prime@ i, {i, PrimeNu@ #}] &@ First@ FirstPosition[s, #] &, t]]