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A049087 Ceiling of mean distance between successive distinct prime divisors of n.

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%I A049087 #11 Jun 26 2021 15:02:12
%S A049087 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 A049087 15,2,1,0,17,10,3,0,3,0,9,2,21,0,1,0,3,14,11,0,1,6,5,16,27,0,2,0,29,4,
%U A049087 0,8,5,0,15,20,3,0,1,0,35,2,17,4,6,0,3,0,39,0,3,12,41,26,9,0,2,6,21,28,45
%N A049087 Ceiling of mean distance between successive distinct prime divisors of n.
%H A049087 Antti Karttunen, <a href="/A049087/b049087.txt">Table of n, a(n) for n = 1..65537</a>
%e A049087 a(105)=2: prime divisors of 105 are 3,5,7; distance between successive pairs: 5-3=2 and 7-5=2; mean of 2 and 2 is 2.
%e A049087 If n=30 the mean is 1.5 and rounding up, a(30)=2.
%t A049087 Table[Ceiling[Mean[Differences[FactorInteger[n][[All,1]]]/.{}->{0,0}]],{n,100}] (* _Harvey P. Dale_, Jun 26 2021 *)
%o A049087 (PARI) A049087(n) = if(1>=omega(n), 0, my(ps = factor(n)[,1], s = 0); for(i=2, #ps, s += (ps[i]-ps[i-1])); ceil(s/(#ps-1))); \\ _Antti Karttunen_, Sep 07 2018
%Y A049087 Cf. also A178921.
%K A049087 easy,nonn
%O A049087 1,10
%A A049087 _Enoch Haga_