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Number of integer triples (x,y,z), x > 0, y > 0, z > 0, such that x <= p, y <= q, z <= r for any factorization n = p*q*r.
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%I #12 Mar 14 2017 00:34:17

%S 1,4,7,13,13,25,19,38,37,49,31,74,37,73,79,104,49,125,55,143,121,121,

%T 67,203,121,145,171,221,85,263,91,272,205,193,199,354,109,217,247,383,

%U 121,398,127,377,381,265,139,531,253,443,331,455,157,558,355,587,373

%N Number of integer triples (x,y,z), x > 0, y > 0, z > 0, such that x <= p, y <= q, z <= r for any factorization n = p*q*r.

%C This sequence is a three-dimensional equivalent of A138808.

%C a(n) >= 3*n-2, with equality iff n is not composite.

%C a(n) >= 3*A138808(n)-3*n+1, with equality iff n has at most 2 prime factors (counted with multiplicity).

%H Rémy Sigrist, <a href="/A283626/b283626.txt">Table of n, a(n) for n = 1..1000</a>

%H Rémy Sigrist, <a href="/A283626/a283626.png">Illustration of the first terms</a>

%o (PARI) a(n)=my(h=matrix(n,n)); fordiv(n,d, fordiv(n/d,dd, for(x=1,d, for(y=1,dd,h[x,y]=max(h[x,y],n/d/dd))))); return(sum(x=1,n, sum(y=1,n,h[x,y])))

%Y Cf. A138808.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Mar 12 2017