

A283626


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.


1



1, 4, 7, 13, 13, 25, 19, 38, 37, 49, 31, 74, 37, 73, 79, 104, 49, 125, 55, 143, 121, 121, 67, 203, 121, 145, 171, 221, 85, 263, 91, 272, 205, 193, 199, 354, 109, 217, 247, 383, 121, 398, 127, 377, 381, 265, 139, 531, 253, 443, 331, 455, 157, 558, 355, 587, 373
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OFFSET

1,2


COMMENTS

This sequence is a threedimensional equivalent of A138808.
a(n) >= 3*n2, with equality iff n is not composite.
a(n) >= 3*A138808(n)3*n+1, with equality iff n has at most 2 prime factors (counted with multiplicity).


LINKS



PROG

(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])))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



