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, 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

Offset: 1

Author

Rémy Sigrist, Mar 12 2017

Keywords

• nonn

Comments

This sequence is a three-dimensional equivalent of A138808.

a(n) >= 3*n-2, 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

• Rémy Sigrist, Table of n, a(n) for n = 1..1000
• Rémy Sigrist, Illustration of the first terms

Crossrefs

Cf. A138808.

Programs

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])))