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

1,3

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A001221, A002110, A004394, A301413.

Sequence in context: A296159 A283334 A301413 * A112179 A058553 A038067

Adjacent sequences: A305053 A305054 A305055 * A305057 A305058 A305059

Keyword

nonn

Author

Michael De Vlieger, Jul 01 2018

Status

approved