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

Author

Juri-Stepan Gerasimov, Mar 28 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A001221, A178139.

Programs

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

PARI

for(n=2, 100, f=omega(n); m=n+1; while(omega(m)!=f, m++); print1(m-n, ", ")) \\ Colin Barker, Jun 27 2014

Formula

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

Extensions

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