A370634 A135507(n) is the product of the first n terms of this sequence.

1, 4, 5, 3, 3, 3, 9, 4, 3, 3, 13, 3, 3, 9, 3, 3, 19, 3, 3, 3, 9, 13, 25, 3, 3, 3, 3, 9, 31, 3, 3, 4, 13, 19, 9, 3, 39, 3, 3, 3, 43, 9, 3, 13, 3, 25, 49, 3, 3, 3, 19, 3, 55, 3, 3, 3, 3, 31, 61, 3, 3, 3, 3, 3, 3, 3, 69, 19, 3, 3, 73, 3, 3, 39, 3, 3, 3, 3, 81, 3

Offset

1,2

Comments

Compactification of A135507 akin to A000705 with respect to A002201.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.

Formula

For n > 1, 3 <= a(n) <= n+2.

For p = A001359(i) such that gcd(a(p-1), p) = 1, a(p) = p+2 = A006512(i).

Example

Table of first 20 terms of this sequence and S = A135507.
   n            S(n)  a(n)
  ------------------------
   1              1     1
   2              4     4
   3             20     5
   4             60     3
   5            180     3
   6            540     3
   7           4860     9
   8          19440     4
   9          58320     3
  10         174960     3
  11        2274480    13
  12        6823440     3
  13       20470320     3
  14      184232880     9
  15      552698640     3
  16     1658095920     3
  17    31503822480    19
  18    94511467440     3
  19   283534402320     3
  20   850603206960     3

Mathematica

nn = 120; j = 1; {1}~Join~Reap[Do[k = 2 j + LCM[j, i]; Sow[k/j]; j = k, {i, 2, nn}] ][[-1, 1]]

Crossrefs

Cf. A001359, A003418, A006512, A135507.

Sequence in context: A057113 A060134 A200351 * A138753 A179410 A272874

Adjacent sequences: A370631 A370632 A370633 * A370635 A370636 A370637

Keyword

nonn

Author

Michael De Vlieger, May 19 2024

Status

approved