A136567 a(n) is the number of exponents occurring only once each in the prime factorization of n.

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, 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, 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

Offset

1,12

Comments

Records are in A006939: 1, 2, 12, 360, 75600, ..., . - Robert G. Wilson v, Jan 20 2008

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A056169(A181819(n)). - Antti Karttunen, Jul 24 2017

Example

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.

Mathematica

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 *)
Table[Boole[n != 1] Count[Split@ Sort[FactorInteger[n][[All, -1]]], _?(Length@ # == 1 &)], {n, 105}] (* Michael De Vlieger, Jul 24 2017 *)

Prog

(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
(Scheme) (define (A136567 n) (A056169 (A181819 n))) ;; Antti Karttunen, Jul 24 2017

Crossrefs

Cf. A056169, A071625, A133924, A136566, A181819.

For a(n)=0 see A130092 plus the term 1; for a(n)=1 see A000961.

Sequence in context: A264893 A340653 A334744 * A336569 A324904 A109708

Adjacent sequences: A136564 A136565 A136566 * A136568 A136569 A136570

Keyword

nonn

Author

Leroy Quet, Jan 07 2008

Extensions

More terms from Robert G. Wilson v, Jan 20 2008

Status

approved