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

Author

Michael De Vlieger, May 19 2024

Keywords

• nonn

Comments

Compactification of A135507 akin to A000705 with respect to A002201.

Examples

			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
		

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.

Crossrefs

Cf. A001359, A003418, A006512, A135507.

Programs

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]]

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).