This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317307 #34 Aug 26 2018 12:35:28 %S A317307 1,3,7,12,15,31,56,63,127,255,511,992,1023,2047,4095,8191,16256,16383, %T A317307 32767,65535,131071,262143,524287,1048575,2097151,4194303,8388607, %U A317307 16777215,33554431,67100672,67108863,134217727,268435455,536870911,1073741823,2147483647,4294967295,8589934591,17179738112,17179869183 %N A317307 Sum of divisors of powers of 2 and sum of divisors of even perfect numbers. %C A317307 Sum of divisors of the numbers k such that the symmetric representation of sigma(k) has only one part, and apart from the central width, the rest of the widths are 1's. %C A317307 Note that the above definition implies that the central width of the symmetric representation of sigma(k) is 1 or 2. For powers of 2 the central width is 1. For even perfect numbers the central width is 2 (see example). %F A317307 a(n) = A000203(A317306(n)). %e A317307 Illustration of initial terms. a(n) is the area (or the number of cells) of the n-th region of the diagram: %e A317307 . _ _ _ _ _ _ _ _ %e A317307 . 1 |_| | | | | | | | | | | | | | %e A317307 . 3 |_ _|_| | | | | | | | | | | | %e A317307 . _ _| _|_| | | | | | | | | | %e A317307 . 7 |_ _ _| _|_| | | | | | | | %e A317307 . _ _ _| _| _ _| | | | | | | %e A317307 . 12 |_ _ _ _| _| | | | | | | %e A317307 . _ _ _ _| | | | | | | | %e A317307 . 15 |_ _ _ _ _| _ _ _| | | | | | %e A317307 . | _ _ _| | | | | %e A317307 . _| | | | | | %e A317307 . _| _| | | | | %e A317307 . _ _| _| | | | | %e A317307 . | _ _| | | | | %e A317307 . | | _ _ _ _ _| | | | %e A317307 . _ _ _ _ _ _ _ _| | | _ _ _ _ _| | | %e A317307 . 31 |_ _ _ _ _ _ _ _ _| | | _ _ _ _ _ _| | %e A317307 . _ _| | | _ _ _ _ _ _| %e A317307 . _ _| _ _| | | %e A317307 . | _| _ _| | %e A317307 . _| _| | _ _| %e A317307 . | _| _| | %e A317307 . _ _ _| | _| _| %e A317307 . | _ _ _| _ _| _| %e A317307 . | | | _ _| %e A317307 . | | _ _ _| | %e A317307 . | | | _ _ _| %e A317307 . _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | %e A317307 . 56 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | %e A317307 . | | %e A317307 . | | %e A317307 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | %e A317307 . 63 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A317307 . %e A317307 The diagram shows the first eight terms of the sequence. The symmetric representation of sigma of the numbers A317306: 1, 2, 4, 6, 8, 16, 28, 32, ..., has only one part, and apart from the central width, the rest of the widths are 1's. %t A317307 DivisorSigma[1, #] &@ Union[2^Range[0, Floor@ Log2@ Last@ #], #] &@ Array[2^(# - 1) (2^# - 1) &@ MersennePrimeExponent@ # &, 7] (* _Michael De Vlieger_, Aug 25 2018, after Robert G. Wilson v at A000396 *) %Y A317307 Union of nonzero terms of A000225 and A139256. %Y A317307 Odd terms give the nonzeros terms of A000225. %Y A317307 Even terms give A139256. %Y A317307 Subsequence of A317305. %Y A317307 Cf. A249351 (the widths). %Y A317307 Cf. A000203, A000396, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A237271, A239660, A239931, A239932, A239933, A239934, A244050, A245092, A262626, A317306. %K A317307 nonn,easy %O A317307 1,2 %A A317307 _Omar E. Pol_, Aug 25 2018