A114707 - OEIS

%I #26 Jun 27 2024 15:23:46

%S 1,2,3,4,5,7,7,8,9,11,11,13,13,15,15,16,17,19,19,21,21,23,23,25,25,27,

%T 27,29,29,32,33,34,36,37,39,40,41,43,45,46,47,50,51,53,55,57,58,59,60,

%U 60,61,63,64,65,66,67,69,71,72,73,74,75,76,76,78,79,80,81,82,84,85,87

%N a(1)=1. For n>1, a(n) = a(n-1) + (number of distinct primes dividing n but not a(n-1)).

%C Number of distinct primes dividing n but not a(n-1) is A114708(n).

%C a(10^k), k=0..6: 1, 11, 130, 1691, 19819, 220501, 2398245. - _Robert G. Wilson v_, Dec 28 2005

%H Robert Israel, <a href="/A114707/b114707.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001221(n*a(n-1)) - A001221(a(n-1)) + a(n-1). - _Jon Maiga_, Jan 09 2019

%e a(11) = 11. Since 2 and 3 are the 2 distinct primes that divide 12 and neither divides 11, a(12) is 2 greater than a(11), a(12) = 13.

%p R:= 1: v:= 1:

%p for n from 2 to 100 do

%p   v:= v + nops(select(p -> v mod p <> 0, numtheory:-factorset(n)));

%p     R:= R,v;

%p od:

%p R; # _Robert Israel_, Jun 27 2024

%t a[1] = 1; a[n_] := a[n] = a[n - 1] + Length@Complement[First /@ FactorInteger@n, First /@ FactorInteger@a[n - 1]]; Array[a, 72] (* _Robert G. Wilson v_, Dec 27 2005 *)

%t a[1] = 1; a[n_] := (m = a[n - 1]; PrimeNu[n*m] - PrimeNu[m] + m); Array[a, 100] (* _Jon Maiga_, Jan 09 2019 *)

%o (PARI) {print1(a=1,",");for(n=2,72,print1(a=a+#setminus(Set(factor(n)[,1]),Set(factor(a)[,1])),","))} \\ _Klaus Brockhaus_, Dec 27 2005

%Y Cf. A001221, A114708.

%K nonn

%O 1,2

%A _Leroy Quet_, Dec 26 2005

%E More terms from _Klaus Brockhaus_ and _Robert G. Wilson v_, Dec 27 2005