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a(n) is the smallest number k such that the symmetric representation of sigma(k) has at least one subpart n.
2

%I #33 Mar 13 2022 19:06:19

%S 1,3,2,7,9,11,4,15,10,19,6,14,24,27,8,31

%N a(n) is the smallest number k such that the symmetric representation of sigma(k) has at least one subpart n.

%C Conjecture: there are infinitely many pairs of the form a(x) = y; a(y) = x (see examples).

%C First differs from A351903 at a(11).

%e For n = 11 we have that 6 is the smallest number k with at least one subpart 11 in the symmetric representation of sigma(k), so a(11) = 6.

%e The symmetric representation of sigma(6) in the first quadrant looks like this:

%e .

%e _ _ _ _

%e |_ _ _ |_ 1

%e | |_|_ 11

%e |_ _ |

%e | |

%e | |

%e |_|

%e .

%e There are one subpart 11 and one subpart 1.

%e .

%e Some pairs of the form a(x) = y; a(y) = x:

%e a(2) = 3; a(3) = 2.

%e a(4) = 7; a(7) = 4.

%e a(6) = 11; a(11) = 6.

%e a(8) = 15; a(15) = 8.

%e a(16) = 31; a(31) = 16.

%e .

%Y Row 1 of A352015.

%Y Cf. A351903 (Analog for parts).

%Y Cf. A000079, A000203, A000225, A001227 (number of subparts), A196020, A235791, A236104, A237270, A237271, A237591, A237593, A279387 (definition of subparts), A280850, A280851 (subparts), A296508, A296513, A347529, A351819.

%K nonn,more

%O 1,2

%A _Omar E. Pol_, Feb 25 2022