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

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, 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, 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

Offset: 1

Author

Alex Ratushnyak, Aug 18 2012

Keywords

• nonn
• easy

Comments

For n <= 41, a(n) = A049087(n).

Links

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

Crossrefs

Cf. A081060, A049087.

Cf. also A137795.

Programs

Mathematica

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 *)
Array[Apply[Times, Differences@ FactorInteger[#][[All, 1]] /. {} -> 0] &, 105] (* Michael De Vlieger, Sep 10 2018 *)

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

Python

from sympy import primerange
primes = list(primerange(2,500))
for n in range(1,100):
    d = n
    prev = 0
    product = 1
    for p in primes:
        if d%p==0:
            if prev:
                product *= p-prev
            while d%p==0:
                d//=p
            if d==1:
                break
            prev = p
    if prev==0:
        product = 0
    print(product, end=',')

Extensions

More terms from Antti Karttunen, Sep 07 2018