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%I A317305 #46 Oct 16 2023 22:25:21
%S A317305 1,3,7,12,15,28,31,39,42,60,56,72,63,91,90,96,124,120,120,168,127,144,
%T A317305 195,186,224,180,234,252,217,210,280,248,360,312,255,336,336,403,372,
%U A317305 392,378,363,480,372,546,508,399,468,465,504,434,576,600,504,504,560,546,744,728,511
%N A317305 Sum of divisors of the n-th number whose divisors increase by a factor of 2 or less.
%C A317305 Also consider the n-th number k with the property that the symmetric representation of sigma(k) has only one part. a(n) is the area of the diagram (see the example). For more information see A237593 and its related sequences.
%H A317305 Paolo Xausa, <a href="/A317305/b317305.txt">Table of n, a(n) for n = 1..10000</a>
%H A317305 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A317305 a(n) = A000203(A174973(n)).
%e A317305 Illustration of initial terms (n = 1..13):
%e A317305 .
%e A317305 a(n)
%e A317305 _ _ _ _ _ _ _ _ _ _ _ _ _
%e A317305 1 |_| | | | | | | | | | | | | | | | | | | | | | | |
%e A317305 3 |_ _|_| | | | | | | | | | | | | | | | | | | | | |
%e A317305 _ _| _|_| | | | | | | | | | | | | | | | | | | |
%e A317305 7 |_ _ _| _|_| | | | | | | | | | | | | | | | | |
%e A317305 _ _ _| _| _ _| | | | | | | | | | | | | | | | |
%e A317305 12 |_ _ _ _| _| _ _ _| | | | | | | | | | | | | | | |
%e A317305 _ _ _ _| | _| _ _| | | | | | | | | | | | | | |
%e A317305 15 |_ _ _ _ _| _| | _ _ _| | | | | | | | | | | | | |
%e A317305 | _| | _ _ _|_| | | | | | | | | | | |
%e A317305 | _ _| _| | _ _ _|_| | | | | | | | | |
%e A317305 _ _ _ _ _ _| | _| _| | _ _ _ _| | | | | | | | |
%e A317305 28 |_ _ _ _ _ _ _| _ _| _| _ _| | _ _ _ _ _| | | | | | | |
%e A317305 | _ _| _| _| | _ _ _ _| | | | | | |
%e A317305 | | | | _ _| | _ _ _ _ _| | | | | |
%e A317305 _ _ _ _ _ _ _ _| | _ _| _ _|_| | | _ _ _ _ _|_| | | |
%e A317305 31 |_ _ _ _ _ _ _ _ _| | _ _| _| _ _| | | _ _ _ _ _|_| |
%e A317305 _ _ _ _ _ _ _ _ _| | | | _| _ _| | | _ _ _ _ _ _|
%e A317305 39 |_ _ _ _ _ _ _ _ _ _| | _ _| _| _ _| _ _| | |
%e A317305 _ _ _ _ _ _ _ _ _ _| | | | | _| _ _| |
%e A317305 42 |_ _ _ _ _ _ _ _ _ _ _| | _ _ _| _| _| | _ _|
%e A317305 | | | _| _| |
%e A317305 | | _ _ _| | _| _|
%e A317305 _ _ _ _ _ _ _ _ _ _ _ _| | | _ _ _| _ _| _|
%e A317305 60 |_ _ _ _ _ _ _ _ _ _ _ _ _| | | | _ _|
%e A317305 | | _ _ _| |
%e A317305 | | | _ _ _|
%e A317305 _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | |
%e A317305 56 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A317305 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A317305 72 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A317305 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A317305 63 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A317305 .
%e A317305 The length of the largest Dyck path of the n-th diagram equals A047836(n).
%e A317305 The semilength equals A174973(n).
%e A317305 a(n) is the area of the n-th diagram.
%t A317305 A317305[upto_]:=Table[If[AllTrue[Map[Last[#]/First[#]&,Partition[Divisors[n],2,1]],#<=2&],DivisorSigma[1,n],Nothing],{n,upto}];
%t A317305 A317305[500] (* _Paolo Xausa_, Jan 12 2023 *)
%Y A317305 A317307 is a subsequence.
%Y A317305 Cf. A174973.
%Y A317305 Cf. A000203, A047836, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A237271, A239660, A239931, A239932, A239933, A239934, A244050, A245092, A262626, A361208.
%K A317305 nonn
%O A317305 1,2
%A A317305 _Omar E. Pol_, Aug 25 2018