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Largest difference between consecutive divisors of n is equal to the sum of divisors of n except 1 and n.
1

%I #22 Feb 15 2020 03:17:03

%S 4,345,6489,88473

%N Largest difference between consecutive divisors of n is equal to the sum of divisors of n except 1 and n.

%C No other term < 600000. - _Emeric Deutsch_, Aug 04 2005

%C No more terms < 10^9. - _Lars Blomberg_, Jun 04 2013

%C If p = 5^k - 2 is a prime > 3, then 3*p*(p+2)/5 is in this sequence (see A109080). - _Charlie Neder_, Oct 13 2018

%C a(5) > 10^13. - _Giovanni Resta_, Feb 15 2020

%e The divisors of 345 are [1, 3, 5, 15, 23, 69, 115, 345] and the largest difference between consecutive divisors is 345-115 = 230; the sum of divisors except 1 and 345 are 3+5+15+23+69+115 = 230.

%p with(numtheory): a:=proc(n) local div: div:=divisors(n): if max(seq(div[j]-div[j-1],j=2..tau(n)))=sigma(n)-1-n then n else fi end: seq(a(n),n=1..100000); # _Emeric Deutsch_, Aug 04 2005

%Y Cf. A048050, A060681.

%K nonn,more

%O 1,1

%A _Jason Earls_, Sep 10 2002

%E More terms from _Emeric Deutsch_, Aug 04 2005