A182286 -id:A182286 - cp's OEIS frontend

A182311 Numbers k such that k is equal to the sum of the proper divisors of k that are greater than k^(1/3).

18, 196, 222, 246, 258, 282, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1398, 1434, 1446, 1506, 1542, 1578, 1614

Offset: 1

Claudio Meller, Apr 24 2012

nonn

On a suggestion of Manuel Valdivia.
Is 407715 the only odd term in this sequence?
407715 is the only odd term < 10^11. - Donovan Johnson, Apr 25 2012

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A182286.

d3[n_] := Total[Select[Most[Divisors[n]], # > n^(1/3) &]]; Select[Range[2, 2000], # == d3[#] &] (* T. D. Noe, Apr 24 2012 *)

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

A182311 Numbers k such that k is equal to the sum of the proper divisors of k that are greater than k^(1/3).

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