Monday, 30 January 2012

Today is 30 day of the year.
30 = 2 x 3 x 5, which is the product of the first three primes.
This product makes 30;

•  the smallest sphenic number.
• Primorial, 5#
• pronic, oblong, rectangular or heteromecic i.e. 5 x 6

30 = 13 + 17, the sum of two consecutive primes.
30 = 1 + 4 + 9 + 16, the sum of the first four squares.

The Aliquot sum of a number, n, is the sum of all the divisors of n. Thus the aliquot sum of 30 = 1 + 2 + 3 + 5 + 6 + 10 + 15  = 42. This then gives rise to an Aliquot sequence where a(n + 1) = aliquot sum of n. Starting with 30 we get a sequence consisting of the 16 numbers 30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0.