%I #24 May 19 2024 13:15:56

%S 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,

%T 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,

%U 3,3,3,3,3,69,19,3,3,73,3,3,39,3,3,3,3,81,3

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

%C Compactification of A135507 akin to A000705 with respect to A002201.

%H Michael De Vlieger, <a href="/A370634/b370634.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A370634/a370634.png">Log log scatterplot of a(n)</a>, n = 1..2^20.

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

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

%e Table of first 20 terms of this sequence and S = A135507.

%e n S(n) a(n)

%e ------------------------

%e 1 1 1

%e 2 4 4

%e 3 20 5

%e 4 60 3

%e 5 180 3

%e 6 540 3

%e 7 4860 9

%e 8 19440 4

%e 9 58320 3

%e 10 174960 3

%e 11 2274480 13

%e 12 6823440 3

%e 13 20470320 3

%e 14 184232880 9

%e 15 552698640 3

%e 16 1658095920 3

%e 17 31503822480 19

%e 18 94511467440 3

%e 19 283534402320 3

%e 20 850603206960 3

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

%Y Cf. A001359, A003418, A006512, A135507.

%K nonn

%O 1,2

%A _Michael De Vlieger_, May 19 2024