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A296512 a(n) is the largest subpart of the symmetric representation of sigma(n).

%I A296512 #56 Jun 18 2025 06:10:44
%S A296512 1,3,2,7,3,11,4,15,5,9,6,23,7,12,8,31,9,35,10,39,11,18,12,47,13,21,14,
%T A296512 55,15,59,16,63,17,27,18,71,19,30,20,79,21,83,22,42,27,36,24,95,25,39,
%U A296512 26,49,27,107,28,111,29,45,30,119,31,48,32,127,33,131,34,63
%N A296512 a(n) is the largest subpart of the symmetric representation of sigma(n).
%C A296512 If n is an odd prime (A065091) then a(n) = (n + 1)/2.
%C A296512 If n is a power of 2 (A000079) then a(n) = 2*n - 1.
%C A296512 If n is a perfect number (A000396) then a(n) = 2*n - 1, assuming there are no odd perfect numbers.
%C A296512 a(n) is also the largest element in the n-th row of the triangles A279391, A280851 and A296508.
%C A296512 The symmetric representation of sigma(n) has A001227(n) subparts.
%C A296512 For the definition of the "subpart" see A279387.
%C A296512 For a diagram with the subparts for the first 16 positive integers see A296508.
%e A296512 For n = 15 the subparts of the symmetric representation of sigma(15) are [8, 7, 1, 8], the largest subpart is 8, so a(15) = 8.
%t A296512 (* a280851[] and support function are defined in A280851 *)
%t A296512 a296512[n_]:=Max[a280851[n]]
%t A296512 Map[a296512,Range[68]] (* _Hartmut F. W. Hoft_, Sep 05 2021 *)
%Y A296512 Shares infinitely many terms with A241558, A241559, A241838, A296513 (and possibly more).
%Y A296512 Cf. A000079, A000203 (sum of subparts), A000225, A000396, A001227 (number of subparts), A065091, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A245092, A279387, A279391, A280850, A280851, A296508.
%K A296512 nonn
%O A296512 1,2
%A A296512 _Omar E. Pol_, Feb 10 2018
%E A296512 More terms from _Omar E. Pol_, Aug 28 2021