OFFSET
1,1
COMMENTS
If also the two consecutive divisors were added to the sum, the first terms would be 18, 55120, 1034540, 1386350, 1675960, ...
EXAMPLE
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.
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.
MAPLE
with(numtheory): P:=proc(q) local a, k, n;
for n from 1 to q do if not isprime(n) then a:=sort([op(divisors(n))]);
for k from 1 to tau(n)-1 do if n=((a[k+1]-1)*a[k+1]-a[k]*(a[k]+1))/2
then print(n); break; fi; od; fi; od; end: P(10^9);
MATHEMATICA
Select[Range[351*10^5], MemberQ[Total[Range[#[[1]]+1, #[[2]]-1]]&/@Partition[ Divisors[ #], 2, 1], #]&] (* Harvey P. Dale, Feb 14 2023 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Apr 26 2018
EXTENSIONS
a(10)-a(30) from Giovanni Resta, Apr 27 2018
STATUS
approved