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

1,1

Comments

A303556 is a subsequence of this sequence.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A055233, A303556.

Sequence in context: A286497 A086830 A084699 * A064483 A365277 A322181

Adjacent sequences: A323438 A323439 A323440 * A323442 A323443 A323444

Keyword

nonn,easy

Author

Paolo P. Lava, Jan 15 2019

Status

approved