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A296512
a(n) is the largest subpart of the symmetric representation of sigma(n).
3
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, 55, 15, 59, 16, 63, 17, 27, 18, 71, 19, 30, 20, 79, 21, 83, 22, 42, 27, 36, 24, 95, 25, 39, 26, 49, 27, 107, 28, 111, 29, 45, 30, 119, 31, 48, 32, 127, 33, 131, 34, 63
OFFSET
1,2
COMMENTS
If n is an odd prime (A065091) then a(n) = (n + 1)/2.
If n is a power of 2 (A000079) then a(n) = 2*n - 1.
If n is a perfect number (A000396) then a(n) = 2*n - 1, assuming there are no odd perfect numbers.
a(n) is also the largest element in the n-th row of the triangles A279391, A280851 and A296508.
The symmetric representation of sigma(n) has A001227(n) subparts.
For the definition of the "subpart" see A279387.
For a diagram with the subparts for the first 16 positive integers see A296508.
EXAMPLE
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.
MATHEMATICA
(* a280851[] and support function are defined in A280851 *)
a296512[n_]:=Max[a280851[n]]
Map[a296512, Range[68] (* Hartmut F. W. Hoft, Sep 05 2021 *)
CROSSREFS
Shares infinitely many terms with A241558, A241559, A241838, A296513 (and possibly more).
Cf. A000079, A000203 (sum of subparts), A000225, A000396, A001227 (number of subparts), A065091, A196020, A235791, A236104, A237048,A 237270, A237271, A237591, A237593, A245092, A279387, A279391, A280850, A280851, A296508.
Sequence in context: A289336 A324509 A335653 * A241558 A295422 A241838
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 10 2018
EXTENSIONS
More terms from Omar E. Pol, Aug 28 2021
STATUS
approved