A188348 Distance between n and the next number with the same number of distinct prime factors.

1, 1, 1, 2, 4, 1, 1, 2, 2, 2, 2, 3, 1, 3, 1, 2, 2, 4, 1, 1, 2, 2, 2, 2, 2, 2, 5, 2, 12, 1, 5, 1, 1, 1, 2, 4, 1, 1, 4, 2, 18, 4, 1, 1, 2, 2, 2, 4, 1, 1, 2, 6, 1, 1, 1, 1, 4, 2, 6, 3, 1, 2, 3, 3, 4, 4, 1, 3, 8, 2, 2, 6, 1, 1, 1, 3, 6, 2, 2, 2, 3, 6, 6, 1, 1, 1, 3, 8, 12

Offset

2,4

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Formula

{min d>0: A001221(n+d) = A001221(n)}.

Maple

N:= 200: # to use numbers up to N
V:= Array(2..N, n -> nops(numtheory:-factorset(n))):
A:= Array(2..N):
for n from 2 to N do
  v:= V[n];
  if assigned(Last[v]) then
     A[Last[v]]:= n-Last[v]
  fi;
  Last[v]:= n;
od:
m:= min(select(t -> A[t]=0, [$2..N]))-1:
seq(A[i], i=2..m); # Robert Israel, Jan 24 2020

Prog

(PARI) a(n) = {my(f=omega(n), m=n+1); while(omega(m)!=f, m++); m-n} \\ Colin Barker, Jun 27 2014

Crossrefs

Cf. A001221, A178139.

Sequence in context: A094643 A094593 A327814 * A336434 A007738 A186520

Adjacent sequences: A188345 A188346 A188347 * A188349 A188350 A188351

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 28 2011

Extensions

Renamed, edited and checked by R. J. Mathar, Mar 28 2011

Status

approved