A130024 a(1)=1. a(n) = number of earlier terms which don't have 2 or more distinct prime divisors in common with n.

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 12, 13, 14, 15, 16, 15, 18, 17, 20, 21, 22, 20, 24, 25, 26, 26, 28, 19, 30, 31, 32, 33, 34, 30, 36, 37, 38, 33, 40, 31, 42, 42, 40, 45, 46, 38, 48, 41, 50, 49, 52, 43, 54, 51, 56, 57, 58, 38, 60, 61, 59, 63, 64, 50, 66, 66, 68, 53, 70, 57, 72

Offset

1,3

Comments

If n is in A354144 then a(n) = n-1. - Robert Israel, Oct 20 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The distinct primes which divide 20 are 2 and 5. So a(20) is the number of earlier terms which are not divisible by at least 2 distinct primes dividing 20; i.e. are not divisible by both 2 and 5. Among the first 19 terms only a(11)=10 and a(12)=10 are divisible by both 2 and 5. There are 17 other earlier terms, so a(20)=17.

Maple

f:= proc(k, S) local t, s;
   t:= 0:
   for s in S do if k mod s = 0 then t:= t+1; if t = 2 then return 0 fi fi od;
   1
end proc:
A[1]:= 1:
for n from 2 to 100 do
   dn:= numtheory:-factorset(n);
   A[n]:= add(f(A[k], dn), k=1..n-1)
od:
seq(A[i], i=1..100); # Robert Israel, Oct 20 2024

Crossrefs

Cf. A131232, A354144.

Sequence in context: A172268 A017895 A228722 * A131232 A297238 A010881

Adjacent sequences: A130021 A130022 A130023 * A130025 A130026 A130027

Keyword

nonn,look

Author

Leroy Quet, Jun 20 2007

Extensions

More terms from Joshua Zucker, Jul 18 2007

Status

approved