A182147 -id:A182147 - cp's OEIS frontend

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

Michel Lagneau, Feb 28 2014

nonn

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).

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

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

Cf. A000203, A066839, A182147, A238502.

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

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

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

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

Better name from Ralf Stephan, Mar 08 2014

A182292 Smallest odd number k such that is equal to the sum of its proper divisors greater than k^(1/n), or 0 if none exist.

Original entry on oeis.org

34155, 407715, 8415

Offset: 2

Manuel Valdivia, Apr 24 2012

a(8) = 159030135. There is no n > 4 for which a(n) is smaller unless a(n) = 0. - Charles R Greathouse IV, Apr 25 2012
Other than a(2) to a(4) and a(8), there is no solution < 2*10^10 for a(n) up to a(1000). - Donovan Johnson, Aug 23 2012
From Alexander Violette, Feb 29 2024: (Start)
a(7) <= 7650499534755.
a(14) <= 221753170660847595. (End)

			The sum proper divisors of 407715 greater than 407715^(1/3) is 77 + 105 + 165 + 231 + 353 + 385 + 1059 + 1155 + 1765 + 2471 + 3883 + 5295 + 7413 + 11649 + 12355 + 19415 + 27181 + 37065 + 58245 + 81543 + 135905 = 407715.

See A182147 for more details for 34155.

Cf. A182311, A182286, A005231.

t={}; d[n_]:= Select[Drop[Divisors[n],-1], #1>n^(1/p)&]; Do[s=Select[Range[1,5*10^5,2], #==Plus@@d[#]&];
  AppendTo[t,s], {p,2,4}]; Flatten[t]

a(n)=my(t,k=8413);while(k+=2,if(sigma(k,-1)>2,if(ispower(k,n,&t),,t=k^(1/n)\1);if(sumdiv(k,d,if(d>t,d))==2*k,return(k)))) \\ Charles R Greathouse IV, Apr 25 2012

cp's OEIS Frontend

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

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