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Sequence of the Day

A003415: , the arithmetic derivative of n: a (0) = a (1) = 0, a ( prime) = 1, a (m n) = m a (n) + n a (m)  .

{ 0, 0, 1, 1, 4, 1, 5, 1, 12, 6, 7, 1, 16, ... }
Based on the product rule for differentiation of functions: for functions and , . So with numbers, . This implies .

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On this day...

 June 21, 1781 Siméon Denis Poisson is born in Pithivers.
 June 21, 1809 Released from an Algerian penal colony, François Arago boards a third ship headed to Marseille, hoping to resume his work measuring the meridian.
 June 21, 1993 At Cambridge, Andrew Wiles gives the first of three lectures about Fermat's last theorem.

Sequences in the news

Sequences in the News
 Feb 01 2018 Alphabet announced a $8,589,869,056 = $A000396(6) stock buyback.
 Jan 03 2018 Largest known term of A000043 announced: 77232917.
 Nov 18 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
 Sep 14 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
 Jan 19 2016 Largest known term of A000043 announced: 274207281, also discovered by Curtis Cooper.
 Mar 02 2014 Fredrik Johansson announces a computation of the partition number p(10 20) ≈ 1.8381765 × 10 11140086259, the largest known term of A000041.
 Dec 06 2013 Microsoft launches a challenge to find large nonMersenne primes, A138837.


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