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Number of ordered triples (a,b,c) of positive integers less than n with the property that n divides a*b*c.
0

%I #28 May 14 2022 22:20:57

%S 0,0,0,7,0,42,0,87,80,156,0,439,0,342,528,687,0,1160,0,1543,1152,930,

%T 0,3207,1024,1332,2024,3319,0,5502,0,4447,3120,2352,4176,9287,0,2970,

%U 4464,10935,0,11724,0,8887,12176,4422,0,19983,4752,12424,7872,12679,0,20330,11280,23271,9936

%N Number of ordered triples (a,b,c) of positive integers less than n with the property that n divides a*b*c.

%C a(n) = 0 iff n is prime or 1.

%e For n = 4 the ordered triples are (1,2,2), (2,1,2), (2,2,1), (2,2,2), (2,2,3), (2,3,2), (3,2,2).

%t Table[Dimensions[Solve[a*b*c == 0 && a != 0 && b != 0 && c != 0, {a, b, c}, Modulus -> n]][[1]], {n, 2, 100}]

%Y Cf. A268631.

%K nonn

%O 1,4

%A _Luca Onnis_, Mar 28 2022