login
A296513
a(n) is the smallest subpart of the symmetric representation of sigma(n).
5
1, 3, 2, 7, 3, 1, 4, 15, 3, 9, 6, 5, 7, 12, 1, 31, 9, 2, 10, 3, 5, 18, 12, 13, 5, 21, 6, 1, 15, 3, 16, 63, 7, 27, 3, 10, 19, 30, 8, 11, 21, 4, 22, 42, 1, 36, 24, 29, 7, 15, 10, 49, 27, 3, 8, 9, 11, 45, 30, 6, 31, 48, 5, 127, 9, 1, 34, 63, 13, 13, 36, 7, 37, 57, 3
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) = 1 assuming there are no odd perfect numbers.
a(n) is also the smallest number in the n-th row of the triangles A279391 and A280851.
a(n) is also the smallest nonzero term in the n-th row of triangle 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.
It appears that a(n) = 1 if and only if n is a hexagonal number (A000384). - Omar E. Pol, Sep 08 2021
The above conjecture is true. See A280851 for a proof. - Omar E. Pol, Mar 10 2022
EXAMPLE
For n = 15 the subparts of the symmetric representation of sigma(15) are [8, 7, 1, 8], the smallest subpart is 1, so a(15) = 1.
MATHEMATICA
(* a280851[] and support function are defined in A280851 *)
a296513[n_]:=Min[a280851[n]]
Map[a296513, Range[75] (* Hartmut F. W. Hoft, Sep 05 2021 *)
CROSSREFS
Shares infinitely many terms with A241558, A241559, A241838, A296512 (and possibly more).
Sequence in context: A308439 A245601 A355934 * A099378 A182885 A182891
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 10 2018
EXTENSIONS
More terms from Omar E. Pol, Aug 28 2021
STATUS
approved