A074844 Largest difference between consecutive divisors of n is equal to the sum of divisors of n except 1 and n.

4, 345, 6489, 88473

Offset: 1

Author

Jason Earls, Sep 10 2002

Keywords

• nonn
• more

Comments

No other term < 600000. - Emeric Deutsch, Aug 04 2005

No more terms < 10^9. - Lars Blomberg, Jun 04 2013

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

a(5) > 10^13. - Giovanni Resta, Feb 15 2020

Examples

			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.
		

Crossrefs

Cf. A048050, A060681.

Programs

Maple

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

Extensions

More terms from Emeric Deutsch, Aug 04 2005