A238535 Sum of divisors d of n where d > sqrt(n).

0, 2, 3, 4, 5, 9, 7, 12, 9, 15, 11, 22, 13, 21, 20, 24, 17, 33, 19, 35, 28, 33, 23, 50, 25, 39, 36, 49, 29, 61, 31, 56, 44, 51, 42, 75, 37, 57, 52, 78, 41, 84, 43, 77, 69, 69, 47, 108, 49, 85, 68, 91, 53, 108, 66, 106, 76, 87, 59, 147, 61, 93, 93, 112, 78, 132

Offset: 1

Author

Michel Lagneau, Feb 28 2014

Keywords

• nonn

Comments

Properties of the sequence:

a(n) = n if n is prime because sigma(n) = n+1 and A066839(n) = 1;

a(p^2) = p^2 if p is prime because sigma(p^2) = p^2+p+1 and A066839(p^2)= p+1 => A000203(p^2) - A066839(p^2)= p^2;

a(m) = 2*m if m = A182147(n) = 42, 54, 66, 78, 102, 114,... (numbers n equal to the sum of its proper divisors greater than square root of n).

Examples

			a(8) = 12 because A000203(8)= 15 and A066839(8) = 3 => 15 - 8 = 12.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A066839, A182147, A238502.

Programs

Mathematica

lst={}; f[n_]:=DivisorSigma[1,n]-Plus@@Select[Divisors@n,#<=Sqrt@n&];Do[If[IntegerQ[f[n]],AppendTo[lst, f[n]]],{n,1,200}];lst

PARI

a(n) = sumdiv(n, d, d*(d>sqrt(n))); \\ Michel Marcus, Feb 28 2014

Sage

def a(n):
    return sum([d for d in Integer(n).divisors() if d>sqrt(n)]) # Ralf Stephan, Mar 08 2014

Formula

a(n) = A000203(n) - A066839(n).

Extensions

Better name from Ralf Stephan, Mar 08 2014