A373938 Number of k in the range s(1), ..., s(n-1) such that gcd(k, s(n)) > 1, where s = A089088.

0, 0, 1, 2, 1, 3, 2, 4, 1, 7, 6, 1, 6, 7, 11, 11, 8, 10, 1, 15, 4, 12, 1, 8, 15, 21, 15, 12, 16, 1, 10, 23, 18, 1, 14, 23, 29, 23, 20, 22, 1, 31, 6, 29, 18, 27, 35, 14, 31, 20, 28, 1, 43, 30, 1, 26, 31, 16, 45, 35, 24, 45, 47, 36, 1, 34, 39, 16, 53, 47, 26, 40, 1, 59, 20, 42, 1, 30, 47, 65, 18

Offset: 0

Author

Scott R. Shannon, Jun 23 2024

Keywords

• nonn

Comments

In the terms studied a(n) = 1 if s(n) is 4 or a prime.

Examples

			a(5) = 5 as A089088(5) = 8 and 8 shares a factor m > 1 with three previous terms, A089088(1) = 2, A089088(2) = 4, and A089088(3) = 6.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 2..2^14.

Crossrefs

Cf. A089088, A373880, A373390, A064413.

Programs

Mathematica

nn = 120; s[0] = 1; s[1] = p = 2; s[2] = i = 4; s[3] = j = 6;
Do[If[PrimeQ[j/2],
    k = Prime[p++],
    k = If[PrimeQ[j], i, j] + 1; While[PrimeQ[k], k++]];
  Set[{s[n], i, j}, {k, j, k}], {n, 4, nn}];
s = Array[s, nn];
{0}~Join~Table[Function[{m, w}, Count[w, _?(! CoprimeQ[#, m[[1]]] &)]] @@
TakeDrop[#, -1] &@  s[[;; n]], {n, nn}] (* Michael De Vlieger, Jun 23 2024 *)