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%I #13 Feb 14 2023 12:56:51
%S 490,55930,98648,222560,396550,584988,838448,1173102,2345720,2855660,
%T 4150120,4781502,5557300,6072460,6115122,6688416,6715280,9390290,
%U 9486950,11691498,12704510,13331240,16035760,17325700,19377050,20055070,20859410,29651748,34516160,35040352
%N Numbers equal to the sum of the numbers between two of their consecutive divisors.
%C If also the two consecutive divisors were added to the sum, the first terms would be 18, 55120, 1034540, 1386350, 1675960, ...
%e a(1) = 490 because 14 and 35 are two consecutive divisors of 490 and the sum of the numbers from 15 to 34 is equal to 490 itself.
%e a(7) = 838448 because 1807 and 2224 are two consecutive divisors of 838448 and the sum of the numbers from 1808 to 2223 is equal to 838448 itself.
%p with(numtheory): P:=proc(q) local a,k,n;
%p for n from 1 to q do if not isprime(n) then a:=sort([op(divisors(n))]);
%p for k from 1 to tau(n)-1 do if n=((a[k+1]-1)*a[k+1]-a[k]*(a[k]+1))/2
%p then print(n); break; fi; od; fi; od; end: P(10^9);
%t Select[Range[351*10^5],MemberQ[Total[Range[#[[1]]+1,#[[2]]-1]]&/@Partition[ Divisors[ #],2,1],#]&] (* _Harvey P. Dale_, Feb 14 2023 *)
%o (PARI) isok(n) = my(d=divisors(n)); vecsearch(vecsort(vector(#d-1, k, ((d[k+1]-1)*d[k+1]-d[k]*(d[k]+1))/2),,8), n); \\ _Michel Marcus_, Apr 27 2018
%Y Cf. A055233.
%K nonn
%O 1,1
%A _Paolo P. Lava_, Apr 26 2018
%E a(10)-a(30) from _Giovanni Resta_, Apr 27 2018
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