A067555 Smallest number m>1 such that the product of the parts in some partition of m is equal to m^n.

2, 16, 27, 45, 60, 72, 96, 108, 128, 144, 162, 180, 216, 216, 240, 243, 288, 288, 324, 324, 360, 384, 405, 432, 432, 480, 486, 486, 540, 540, 576, 576, 640, 648, 648, 648, 720, 729, 729, 729, 810, 810, 864, 864, 864, 960, 960, 960, 972, 972, 972, 1080, 1080

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Formula

Let the prime factorization of m be product{p_i}. a(n)=m is the least number such that m >= sum{p_i} * n . - Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Aug 16 2006

Example

For n = 2, m = 16 = 2+2+2+2+2+2+2+2, 2^8 = 16^2. so a(2) = 16.

Crossrefs

Cf. A000041.

Sequence in context: A276069 A190046 A067566 * A108705 A113933 A127871

Adjacent sequences: A067552 A067553 A067554 * A067556 A067557 A067558

Keyword

nonn

Author

Naohiro Nomoto, Jan 29 2002

Extensions

More terms from Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Aug 16 2006

Status

approved