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