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A178921
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Product of distances between successive distinct prime divisors of n; zero if n has only 1 distinct prime factor.
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2
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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
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OFFSET
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1,10
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COMMENTS
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For n <= 41, a(n) = A049087(n).
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537
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MATHEMATICA
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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 *)
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PROG
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(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=', ')
(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
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CROSSREFS
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Cf. A081060, A049087.
Cf. also A137795.
Sequence in context: A300228 A100573 A049087 * A046665 A100574 A342122
Adjacent sequences: A178918 A178919 A178920 * A178922 A178923 A178924
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KEYWORD
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nonn,easy
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AUTHOR
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Alex Ratushnyak, Aug 18 2012
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EXTENSIONS
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More terms from Antti Karttunen, Sep 07 2018
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STATUS
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approved
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