Template:Sequence of the Day for July 20

Intended for: July 20, 2012

Timetable

• First draft entered by Alonso del Arte on April 20, 2011 ✓
• Draft reviewed by Alonso del Arte on July 16, 2011 ✓
• Draft approved by Daniel Forgues on June 20, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A007955: Product of divisors of

n, n   ≥   1

.

n ∏   i  = 1 i ∣ n    i  =    n ∏   i  = 1      i [i ∣ n], n ≥ 1.

where [⋅] is the Iverson bracket.

{ 1, 2, 3, 8, 5, 36, 7, ... }

In Only Problems, Not Solutions!, Florentin Smarandache lists this sequence (page 24), describes it, and urges the reader to study it, saying nothing else. It is easy enough to see that each prime number

p

will occur once and only once in this sequence, namely, at

a (p)

. T. D. Noe goes much further than that and actually proves that each term of this sequence occurs just once. Of course not every positive integer occurs in this sequence (e.g., squares of primes). The product of divisors of

n

is sometimes called the divisorial of

n

.