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A296513
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a(n) is the smallest subpart of the symmetric representation of sigma(n).
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4
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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(* a280851[] and support function are defined in A280851 *)
a296513[n_]:=Min[a280851[n]]
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CROSSREFS
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Cf. A000079, A000203 (sum of subparts), A000225, A000384, A000396, A001227 (number of subparts), A065091, A099378, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A245092, A279387, A279391, A280850, A280851, A296508.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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