A323441 Numbers equal to the sum of the numbers between two of their divisors.

12, 30, 60, 90, 108, 180, 234, 240, 390, 408, 420, 462, 480, 490, 630, 756, 840, 880, 900, 945, 1122, 1218, 1248, 1430, 1500, 1512, 1560, 1584, 1998, 2070, 2100, 2310, 2460, 2520, 2652, 2660, 2970, 3306, 3330, 3528, 3780, 3960, 4004, 4032, 4134, 4140, 4275, 4788

Offset: 1

Author

Paolo P. Lava, Jan 15 2019

Keywords

• nonn
• easy

Comments

A303556 is a subsequence of this sequence.

Examples

			Divisors of 12 are 1, 2, 3, 4, 6, 12 and the sum of the numbers between 2 and 6 is 3 + 4 + 5 = 12.
Divisors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 and the sum of the numbers between 9 and 18 is 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 = 108.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055233, A303556.

Programs

Maple

with(numtheory): P:=proc(n) local a, j, k; a:=sort([op(divisors(n))]);
for j from 1 to nops(a)-1 do for k from j+1 to nops(a) do
if n=((a[k]-1)*a[k]-a[j]*(a[j]+1))/2 then RETURN(n); fi;
od; od; end: seq(P(i), i=2..10^4);

Mathematica

Select[Range[5000], MemberQ[Union@ Map[Total@ Range[#1 + 1, #2 - 1] & @@ # &, Subsets[Divisors@ #, {2}]], #] &] (* Michael De Vlieger, Jan 18 2019 *)