A076398 Number of distinct prime factors of n-th perfect power.

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

Offset

1,9

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Perfect Powers.

Eric Weisstein's World of Mathematics, Distinct Prime Factors.

Formula

a(n) = A001221(A001597(n)).

a(n) = A001221(A025478(n)).

Mathematica

ppQ[1] = True; ppQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1; PrimeNu /@ Select[Range[10^4], ppQ] (* Jean-François Alcover, Jul 15 2017 *)

Prog

(Haskell)
a076398 = a001221 . a025478  -- Reinhard Zumkeller, Mar 28 2014
(PARI) lista(nn) = for(n=1, nn, if ((n==1) || ispower(n), print1(omega(n), ", "))); \\ Michel Marcus, Jul 15 2017

Crossrefs

Cf. A001221, A001597, A025478, A076399, A076400.

Sequence in context: A205788 A214054 A330739 * A086257 A161098 A354999

Adjacent sequences: A076395 A076396 A076397 * A076399 A076400 A076401

Keyword

nonn

Author

Reinhard Zumkeller, Oct 09 2002

Status

approved