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A351904 a(n) is the smallest number k such that the symmetric representation of sigma(k) has at least one subpart n.

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%I A351904 #33 Mar 13 2022 19:06:19
%S A351904 1,3,2,7,9,11,4,15,10,19,6,14,24,27,8,31
%N A351904 a(n) is the smallest number k such that the symmetric representation of sigma(k) has at least one subpart n.
%C A351904 Conjecture: there are infinitely many pairs of the form a(x) = y; a(y) = x (see examples).
%C A351904 First differs from A351903 at a(11).
%e A351904 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 A351904 The symmetric representation of sigma(6) in the first quadrant looks like this:
%e A351904 .
%e A351904    _ _ _ _
%e A351904   |_ _ _  |_ 1
%e A351904         | |_|_ 11
%e A351904         |_ _  |
%e A351904             | |
%e A351904             | |
%e A351904             |_|
%e A351904 .
%e A351904 There are one subpart 11 and one subpart 1.
%e A351904 .
%e A351904 Some pairs of the form a(x) = y; a(y) = x:
%e A351904    a(2) =  3;   a(3) =  2.
%e A351904    a(4) =  7;   a(7) =  4.
%e A351904    a(6) = 11;  a(11) =  6.
%e A351904    a(8) = 15;  a(15) =  8.
%e A351904   a(16) = 31;  a(31) = 16.
%e A351904 .
%Y A351904 Row 1 of A352015.
%Y A351904 Cf. A351903 (Analog for parts).
%Y A351904 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 A351904 nonn,more
%O A351904 1,2
%A A351904 _Omar E. Pol_, Feb 25 2022