A101423 Number of different cuboids with volume p^3 * q^n, where p,q are distinct prime numbers.

3, 6, 12, 19, 28, 38, 51, 64, 80, 97, 116, 136, 159, 182, 208, 235, 264, 294, 327, 360, 396, 433, 472, 512, 555, 598, 644, 691, 740, 790, 843, 896, 952, 1009, 1068, 1128, 1191, 1254, 1320, 1387, 1456, 1526, 1599, 1672, 1748, 1825, 1904, 1984, 2067, 2150, 2236

Offset: 0

Author

Anthony C Robin, Jan 17 2005

Keywords

• nonn

Comments

Subsequence of A034836, which gives the number of cuboids for volume n.

Crossrefs

Cf. A034836, A101424, A101425, A101426, A101427.

Formula

a(n) = A034836(2^3*3^n) = A034836(3^3*2^n) = A034836(p^3*q^n) for p,q distinct primes.

Empirical g.f.: -(x^3+3*x^2+3*x+3)/((x+1)*(x^2+x+1)*(x-1)^3). - Colin Barker, Mar 28 2014

Extensions

Corrected, edited and extended by Ray Chandler, Dec 19 2008

a(0)=3 prepended and g.f. edited by Alois P. Heinz, Oct 05 2016