A114708 a(n) = A114707(n) - A114707(n-1) = the number of distinct primes dividing n but not A114707(n-1).

1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 3, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 1, 3, 1, 2, 3, 1

Offset

2,5

Comments

First occurrence of k=0..8: 7, 2, 6, 30, 330, 4620, 46410, 570570, ..., . - Robert G. Wilson v, Dec 28 2005

Links

Table of n, a(n) for n=2..106.

Example

A114707(11) = 11. Since 2 and 3 are the 2 distinct primes that divide 12 and neither divides 11, a(12) is 2 (and A114707(12) is 2 + A114707(11) = 13).

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + Length@Complement[First /@ FactorInteger@n, First /@ FactorInteger@a[n - 1]]; b = Array[a, 100]; Drop[b, 1] - Drop[b, -1] (* Robert G. Wilson v, Dec 28 2005 *)

Prog

(PARI) {a=1; for(n=2, 106, print1(d=#setminus(Set(factor(n)[, 1]), Set(factor(a)[, 1])), ", "); a=a+d)} \\ Klaus Brockhaus, Dec 27 2005

Crossrefs

Cf. A114707.

Sequence in context: A178146 A305435 A350658 * A084927 A333750 A072670

Adjacent sequences: A114705 A114706 A114707 * A114709 A114710 A114711

Keyword

nonn

Author

Leroy Quet, Dec 26 2005

Extensions

More terms from Klaus Brockhaus and Robert G. Wilson v, Dec 27 2005

Status

approved