|
%I #19 Jul 26 2017 09:23:41
%S 0,1,1,1,1,0,1,1,1,0,1,2,1,0,0,1,1,2,1,2,0,0,1,2,1,0,1,2,1,0,1,1,0,0,
%T 0,0,1,0,0,2,1,0,1,2,2,0,1,2,1,2,0,2,1,2,0,2,0,0,1,1,1,0,2,1,0,0,1,2,
%U 0,0,1,2,1,0,2,2,0,0,1,2,1,0,1,1,0,0,0,2,1,1,0,2,0,0,0,2,1,2,2,0,1,0,1,2,0
%N a(n) is the number of exponents occurring only once each in the prime factorization of n.
%C Records are in A006939: 1, 2, 12, 360, 75600, ..., . - _Robert G. Wilson v_, Jan 20 2008
%H Antti Karttunen, <a href="/A136567/b136567.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(n) = A056169(A181819(n)). - _Antti Karttunen_, Jul 24 2017
%e 4200 = 2^3 * 3^1 * 5^2 * 7^1. The exponents of the prime factorization are therefore 3,1,2,1. The exponents occurring exactly once are 2 and 3. So a(4200) = 2.
%t f[n_] := Block[{fi = Sort[Last /@ FactorInteger@n]}, Count[ Count[fi, # ] & /@ Union@fi, 1]]; f[1] = 0; Array[f, 105] (* _Robert G. Wilson v_, Jan 20 2008 *)
%t Table[Boole[n != 1] Count[Split@ Sort[FactorInteger[n][[All, -1]]], _?(Length@ # == 1 &)], {n, 105}] (* _Michael De Vlieger_, Jul 24 2017 *)
%o (PARI) A136567(n) = { my(exps=(factor(n)[, 2]), m=prod(i=1, length(exps), prime(exps[i])), f=factor(m)[, 2]); sum(i=1, #f, f[i]==1); }; \\ _Antti Karttunen_, Jul 24 2017
%o (Scheme) (define (A136567 n) (A056169 (A181819 n))) ;; _Antti Karttunen_, Jul 24 2017
%Y Cf. A056169, A071625, A133924, A136566, A181819.
%Y For a(n)=0 see A130092 plus the term 1; for a(n)=1 see A000961.
%K nonn
%O 1,12
%A _Leroy Quet_, Jan 07 2008
%E More terms from _Robert G. Wilson v_, Jan 20 2008
|
