A121599 - OEIS

%I #14 May 11 2020 18:47:13

%S 1,1,2,2,4,2,6,2,7,3,10,4,12,4,11,5,16,6,18,6,14,6,22,6,22,6,17,7,28,

%T 8,30,8,22,8,31,9,36,10,26,10,40,10,42,10,31,11,46,12,43,13,36,14,52,

%U 14,46,14,41,15,58,16,60,16,45,17,53,19,66,20,49,21,70,22,72,22,53,23,65

%N a(n) = number of earlier terms which are not divisible by the smallest prime dividing n, for n >= 2, with a(1) = 1.

%F a(p) = p - 1 for p prime. - _Petros Hadjicostas_, May 11 2020

%e 2 is the smallest prime dividing 12. Among the first 11 terms of the sequence there are 4 terms (1, 1, 7, 3) that are not divisible by 2. So a(12) = 4.

%t f[s_] := Append[s, Length@ Select[s, Mod[ #, FactorInteger[1 + Length@s][[1, 1]]] != 0 &]]; Nest[f, {1}, 76] (* _Robert G. Wilson v_ *)

%o (PARI) {m=78;print1(a=1,",");v=[a];for(n=2,m,p=factor(n)[1,1];a=0;for(j=1,n-1,if(v[j]%p>0,a++));print1(a,",");v=concat(v,a))} \\ _Klaus Brockhaus_, Aug 15 2006

%Y Cf. A096216, A121600.

%K nonn

%O 1,3

%A _Leroy Quet_, Aug 09 2006

%E More terms from _Klaus Brockhaus_ and _Robert G. Wilson v_, Aug 15 2006