A265999 Numbers k such that in the symmetric representation of sigma(k) all parts are of the same size.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 52, 53, 54, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 71, 72, 73, 74, 76, 78, 79, 80, 82, 83, 84, 86, 88, 89, 90, 92, 94, 96, 97, 100

Offset

1,2

Comments

All powers of 2, all prime numbers and all even perfect numbers are members of this sequence.

For more information about the symmetric representation of sigma see A237270 and A237593.

Sequence A174973: the symmetric representation of sigma, SRS(A174973(n)) consisting of 1 part, and sequence A239929: SRS(A239929(n)) consisting of 2 parts, are proper subsequences. Sequence A251820: SRS(A251820(n)) consisting of 3 equal parts, contains the only other known members 15 and 5950 of this sequence. No number m with SRS(m) consisting of 4 or more equal parts is known. - Hartmut F. W. Hoft, Jan 11 2025

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

9 is not in the sequence because the parts of the symmetric representation of sigma(9) = 13 are [5, 3, 5].
10 is in the sequence because the parts of the symmetric representation of sigma(10) = 18 are [9, 9].
SRS(15) = { 8, 8, 8 } and SRS(5950) = { 4464, 4464, 4464 }. - Hartmut F. W. Hoft, Jan 11 2025

Mathematica

(* Function partsSRS[ ] is defined in A377654 *)
a265999[n_] := Select[Range[n], Length[Union[partsSRS[#]]]==1&]
a265999[100] (* Hartmut F. W. Hoft, Jan 11 2025 *)

Crossrefs

Cf. A000040, A000079, A000203, A000396, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A245092, A262626, A266000.

Cf. A174973, A239929, A251820, A377654.

Sequence in context: A324721 A327534 A305732 * A316502 A316495 A356316

Adjacent sequences: A265996 A265997 A265998 * A266000 A266001 A266002

Keyword

nonn

Author

Omar E. Pol, Dec 19 2015

Status

approved