cp's OEIS Frontend

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

%I A265999 #45 Jan 23 2025 15:36:03
%S A265999 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,
%T A265999 30,31,32,34,36,37,38,40,41,42,43,44,46,47,48,52,53,54,56,58,59,60,61,
%U A265999 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
%N A265999 Numbers k such that in the symmetric representation of sigma(k) all parts are of the same size.
%C A265999 All powers of 2, all prime numbers and all even perfect numbers are members of this sequence.
%C A265999 For more information about the symmetric representation of sigma see A237270 and A237593.
%C A265999 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
%H A265999 Michael De Vlieger, <a href="/A265999/b265999.txt">Table of n, a(n) for n = 1..10000</a>
%e A265999 9 is not in the sequence because the parts of the symmetric representation of sigma(9) = 13 are [5, 3, 5].
%e A265999 10 is in the sequence because the parts of the symmetric representation of sigma(10) = 18 are [9, 9].
%e A265999 SRS(15) = { 8, 8, 8 } and SRS(5950) = { 4464, 4464, 4464 }. - _Hartmut F. W. Hoft_, Jan 11 2025
%t A265999 (* Function partsSRS[ ] is defined in A377654 *)
%t A265999 a265999[n_] := Select[Range[n], Length[Union[partsSRS[#]]]==1&]
%t A265999 a265999[100] (* _Hartmut F. W. Hoft_, Jan 11 2025 *)
%Y A265999 Cf. A000040, A000079, A000203, A000396, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A245092, A262626, A266000.
%Y A265999 Cf. A174973, A239929, A251820, A377654.
%K A265999 nonn
%O A265999 1,2
%A A265999 _Omar E. Pol_, Dec 19 2015