Template:Sequence of the Day for February 12

Intended for: February 12, 2014

Timetable

• First draft entered by Alonso del Arte on November 6, 2011 ✓
• Draft reviewed by Daniel Forgues on February 12, 2012 ✓
• Draft approved by Alonso del Arte on November 11, 2013 ✓

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.

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A002046: Larger number

n

of amicable pair

(m, n)

of numbers.

{ 284, 1210, 2924, 5564, 6368, 10856, 14595, ... }

Two integers

m

and

n

are amicable numbers (amicable pair of numbers) if

σ (m)  −  m = n

and

σ (n)  −  n = m

.

These larger numbers of amicable pairs are of course deficient numbers, while the smallest numbers of amicable pairs are abundant numbers. One might say that the pair is mutually perfect (so to speak) since the abundancy of the smaller number cancels out the deficiency of the larger number, i.e.

σ (m) + σ (n)  =  2 (m + n).