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A347273
Number of positive widths in the symmetric representation of sigma(n).
2
1, 3, 4, 7, 6, 11, 8, 15, 13, 18, 12, 23, 14, 24, 23, 31, 18, 35, 20, 39, 32, 36, 24, 47, 31, 42, 40, 55, 30, 59, 32, 63, 48, 54, 45, 71, 38, 60, 56, 79, 42, 83, 44, 84, 73, 72, 48, 95, 57, 93, 72, 98, 54, 107, 72, 111
OFFSET
1,2
COMMENTS
a(n) is also the number of columns that contain ON cells in the ziggurat diagram of n. Both diagrams can be unified in a three-dimensional version.
a(n) is also the number of nonzero terms in the n-th row of A249351.
The number of widths in the symmetric representation of sigma(n) is equal to 2*n - 1 = A005408(n-1).
The sum of the positive widths (also the sum of all widths) of the symmetric representation of sigma(n) equals A000203(n).
Indices where a(n) = 2*n - 1 give A174973 and also A238443.
a(p) = p + 1, if p is prime.
a(n) = 2*n - 1, if and only if A237271(n) = 1.
a(n) = A000203(n) if n is a member of A174905.
For the definition of "width" see A249351.
FORMULA
a(n) = A005408(n-1) - A347361(n).
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Aug 29 2021
STATUS
approved