A155085 -id:A155085 - cp's OEIS frontend

A114071 sigma(n) + n is a fourth power.

33, 7153, 16065, 29976, 36673, 39169, 117985, 849385, 2475045, 2757073, 5421336, 7137025, 9474784, 10797120, 11596833, 13627248, 15714240, 25586785, 26821458, 28849249, 37001785, 40441441, 43751896, 69748561, 70338768, 95516836

Offset: 1

Giovanni Resta, Feb 13 2006

nonn

			sigma(33) + 33 = 81 = 3^4.

Cf. A155085, subsequence of A114069.

isok(n) = ispower(sigma(n) + n, 4); \\ Michel Marcus, Jan 09 2014

a(9)-a(26) from Donovan Johnson, Feb 01 2009

A387001 Number of vertices in the diagram called "symmetric representation of sigma(n)" where its "parts" or polygons are dissected into unit squares (see the example).

Original entry on oeis.org

4, 8, 11, 16, 17, 25, 23, 32, 32, 39, 35, 53, 41, 53, 55, 64, 53, 76, 59, 83, 75, 81, 71, 109, 82, 95, 95, 113, 89, 133, 95, 128, 115, 123, 119, 164, 113, 137, 135, 171, 125, 181, 131, 173, 169, 165, 143, 221, 156, 194, 175, 203, 161, 229, 183, 233, 195, 207, 179, 289, 185, 221, 231, 256

Offset: 1

Omar E. Pol, Aug 14 2025

nonn

Consider here that in the diagram every edge has length 1 and every face is a unit square.
The number of faces is A000203(n).
The number of edges is 2*A155085(n).
The number of edges with the same orientation is A155085(n).

			For n = 5 the diagram is as shown below:
   _ _ _
  |_|_|_|
        |_ _
          |_|
          |_|
          |_|
.
The number of vertices is a(5) = 17.
The number of faces is A000203(5) = 6.
The number of edges is 2*A155085(5) = 2*11 = 22.
The number of edges with the same orientation is A155085(5) = 11.

Omar E. Pol, Illustration of initial terms of A000203 in a concave polyhedron (n = 1..16)

Cf. A000203, A005408, A155085, A224880, A237270, A237271, A237593.

a(n) = A000203(n) + A005408(n).
a(n) = 2*A155085(n) - A000203(n) + 1. (Euler's formula: V = E - F + 1).
a(n) = A224880(n) + 1.

cp's OEIS Frontend

A114071 sigma(n) + n is a fourth power.

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A387001 Number of vertices in the diagram called "symmetric representation of sigma(n)" where its "parts" or polygons are dissected into unit squares (see the example).

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