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A178921 Product of distances between successive distinct prime divisors of n; zero if n has only 1 distinct prime factor.

%I A178921 #27 May 20 2021 08:19:55
%S A178921 0,0,0,0,0,1,0,0,0,3,0,1,0,5,2,0,0,1,0,3,4,9,0,1,0,11,0,5,0,2,0,0,8,
%T A178921 15,2,1,0,17,10,3,0,4,0,9,2,21,0,1,0,3,14,11,0,1,6,5,16,27,0,2,0,29,4,
%U A178921 0,8,8,0,15,20,6,0,1,0,35,2,17,4,10,0,3,0,39,0,4,12,41,26,9,0,2,6,21,28,45,14,1,0,5,8,3,0,14,0,11
%N A178921 Product of distances between successive distinct prime divisors of n; zero if n has only 1 distinct prime factor.
%C A178921 For n <= 41, a(n) = A049087(n).
%H A178921 Antti Karttunen, <a href="/A178921/b178921.txt">Table of n, a(n) for n = 1..65537</a>
%t A178921 f[n_] := Module[{ps}, If[n <= 1, 0, ps = Transpose[FactorInteger[n]][[1]]; Times @@ Differences[ps]]]; Table[f[n], {n, 100}] (* _T. D. Noe_, Aug 20 2012 *)
%t A178921 Array[Apply[Times, Differences@ FactorInteger[#][[All, 1]] /. {} -> 0] &, 105] (* _Michael De Vlieger_, Sep 10 2018 *)
%o A178921 (Python)
%o A178921 from sympy import primerange
%o A178921 primes = list(primerange(2,500))
%o A178921 for n in range(1,100):
%o A178921     d = n
%o A178921     prev = 0
%o A178921     product = 1
%o A178921     for p in primes:
%o A178921         if d%p==0:
%o A178921             if prev:
%o A178921                 product *= p-prev
%o A178921             while d%p==0:
%o A178921                 d//=p
%o A178921             if d==1:
%o A178921                 break
%o A178921             prev = p
%o A178921     if prev==0:
%o A178921         product = 0
%o A178921     print(product, end=',')
%o A178921 (PARI) A178921(n) = if(1>=omega(n), 0, my(ps = factor(n)[,1], m = 1); for(i=2, #ps, m *= (ps[i]-ps[i-1])); (m)); \\ _Antti Karttunen_, Sep 07 2018
%Y A178921 Cf. A081060, A049087.
%Y A178921 Cf. also A137795.
%K A178921 nonn,easy
%O A178921 1,10
%A A178921 _Alex Ratushnyak_, Aug 18 2012
%E A178921 More terms from _Antti Karttunen_, Sep 07 2018