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A081060 Product of differences of distinct prime factors of n.

%I A081060 #16 Aug 10 2018 09:05:40
%S A081060 1,1,1,1,1,1,1,1,1,3,1,1,1,5,2,1,1,1,1,3,4,9,1,1,1,11,1,5,1,6,1,1,8,
%T A081060 15,2,1,1,17,10,3,1,20,1,9,2,21,1,1,1,3,14,11,1,1,6,5,16,27,1,6,1,29,
%U A081060 4,1,8,72,1,15,20,30,1,1,1,35,2,17,4,110,1,3,1,39,1,20,12,41,26,9,1,6,6,21,28
%N A081060 Product of differences of distinct prime factors of n.
%C A081060 a(n)=1 iff n is 3-smooth (A003586) or n is a prime power (A000961), see A081061;
%C A081060 a(A006881(k)) > 1 for k > 1; if a(n) > 1 then A079275(n) > 0.
%C A081060 From _Robert G. Wilson v_, Aug 06 2018: (Start)
%C A081060 First occurrence of k, k=1,2,3,... or 0 if impossible: 1, 15, 10, 21, 14, 30, 0, 33, 22, 39, 26, 85, 0, 51, 34, 57, 38, 115, ..., ;
%C A081060 Impossible values: 7, 13, 19, 23, 25, 31, 33, 37, 43, 47, 49, 53, 55, 61, 63, 67, 73, 75, 79, 83, 85, 89, 91, 93, 97, ..., ;
%C A081060 Records: 1, 3, 5, 9, 11, 15, 17, 20, 21, 27, 29, 72, 110, 210, 272, 420, 540, 702, 812, 1190, 1482, 1640, 1980, 2262, 2550, 2592, 3192, 3422, 5280, 5760, 5852, ..., .
%C A081060 (End).
%H A081060 Antti Karttunen, <a href="/A081060/b081060.txt">Table of n, a(n) for n = 1..65537</a>
%F A081060 a(n) = Product(abs(p-q): p, q distinct prime factors of n).
%e A081060 a(42) = a(2*3*7) = |2-3|*|2-7|*|3-7| = 1*5*4 = 20.
%t A081060 a[n_] := Times @@ Flatten[Differences@# & /@ Subsets[First@# & /@ FactorInteger@n, {2}]]; Array[a, 90] (* _Robert G. Wilson v_, Aug 06 2018 *)
%o A081060 (PARI) A081060(n) = if(omega(n)<=1,1,my(ps = factor(n)[, 1]~, m=1); for(i=1,(#ps)-1,for(j=i+1,#ps, m *= (ps[j]-ps[i]))); (m)); \\ _Antti Karttunen_, Aug 06 2018
%K A081060 nonn
%O A081060 1,10
%A A081060 _Reinhard Zumkeller_, Mar 04 2003