A136177 Number of exponents in the prime factorization of n that are coprime to n.

0, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 0, 1, 1, 3, 1, 1, 2, 2, 2, 0, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 0, 2, 3, 1, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 0, 1, 3, 1, 2, 3

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

8000 = 2^6 * 5^3. 6 is not coprime to 8000, but 3 is. So a(8000) = 1.

Mathematica

Table[Length[Select[Table[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}], GCD[ #, n] == 1 &]], {n, 2, 90}] (* Stefan Steinerberger, Dec 21 2007 *)
Join[{0}, Table[Count[FactorInteger[n][[All, 2]], _?(CoprimeQ[#, n]&)], {n, 2, 110}]] (* Harvey P. Dale, Aug 05 2018 *)

Prog

(PARI) A136177(n)={local(t); sum(j=1, #t=factor(n)[, 2]~, gcd(n, t[j])==1)} \\ M. F. Hasler, Dec 21 2007

Crossrefs

Cf. A136176.

Sequence in context: A086257 A161098 A354999 * A212178 A322818 A382857

Adjacent sequences: A136174 A136175 A136176 * A136178 A136179 A136180

Keyword

nonn,easy

Author

Leroy Quet, Dec 19 2007

Extensions

More terms from M. F. Hasler and Stefan Steinerberger, Dec 21 2007

Status

approved