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A206026 a(n) = smallest number m such that sigma(k) = m has at least n positive solutions k.

%I A206026 #16 Dec 16 2024 02:01:03
%S A206026 1,12,24,72,72,168,240,336,360,504,576,720,720,720,720,1440,1440,1440,
%T A206026 1440,1440,1440,2880,2880,2880,2880,2880,2880,2880,2880,4320,4320,
%U A206026 4320,4320,4320,4320,5760,5760,8640,8640,8640,8640,8640,8640,8640,8640,8640,8640
%N A206026 a(n) = smallest number m such that sigma(k) = m has at least n positive solutions k.
%C A206026 Sequence of numbers from A145899.
%H A206026 Amiram Eldar, <a href="/A206026/b206026.txt">Table of n, a(n) for n = 1..1000</a>
%H A206026 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A206026 a(6) = 168 because 168 is the smallest value of sigma(k) for n = 6 positive integers k such that sigma(k) = 168 has solution; k = 60, 78, 92, 123, 143, 167.
%o A206026 (PARI) list(len) = {my(v = vector(len), k = 1, c = 0, i); while(c < len, i = invsigmaNum(k); for(j = 1, i, if(j <= len && v[j] == 0, v[j] = k; c++)); k++); v;} \\ _Amiram Eldar_, Dec 15 2024, using _Max Alekseyev_'s invphi.gp
%Y A206026 Cf. A000203, A054973, A085790, A145899, A206027.
%K A206026 nonn
%O A206026 1,2
%A A206026 _Jaroslav Krizek_, Feb 03 2012