A323441 - OEIS

%I #15 Jan 29 2019 06:29:22

%S 12,30,60,90,108,180,234,240,390,408,420,462,480,490,630,756,840,880,

%T 900,945,1122,1218,1248,1430,1500,1512,1560,1584,1998,2070,2100,2310,

%U 2460,2520,2652,2660,2970,3306,3330,3528,3780,3960,4004,4032,4134,4140,4275,4788

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

%C A303556 is a subsequence of this sequence.

%H Paolo P. Lava, <a href="/A323441/b323441.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%e 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.

%p with(numtheory): P:=proc(n) local a, j, k; a:=sort([op(divisors(n))]);

%p for j from 1 to nops(a)-1 do for k from j+1 to nops(a) do

%p if n=((a[k]-1)*a[k]-a[j]*(a[j]+1))/2 then RETURN(n); fi;

%p od; od; end: seq(P(i), i=2..10^4);

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

%Y Cf. A055233, A303556.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Jan 15 2019