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A136567 a(n) is the number of exponents occurring only once each in the prime factorization of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 05:25 EDT 2021. Contains 345080 sequences. (Running on oeis4.)