A303556 Numbers equal to the sum of the numbers between two of their consecutive divisors.

490, 55930, 98648, 222560, 396550, 584988, 838448, 1173102, 2345720, 2855660, 4150120, 4781502, 5557300, 6072460, 6115122, 6688416, 6715280, 9390290, 9486950, 11691498, 12704510, 13331240, 16035760, 17325700, 19377050, 20055070, 20859410, 29651748, 34516160, 35040352

Offset: 1

Author

Paolo P. Lava, Apr 26 2018

Keywords

• nonn

Comments

If also the two consecutive divisors were added to the sum, the first terms would be 18, 55120, 1034540, 1386350, 1675960, ...

Examples

			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.
		

Crossrefs

Cf. A055233.

Programs

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 *)

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

Extensions

a(10)-a(30) from Giovanni Resta, Apr 27 2018