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A247956 a(n) is the smallest number k such that sigma(k) = 2^n or 0 if no such k exists.

%I A247956 #47 Dec 31 2024 06:33:24
%S A247956 1,0,3,7,0,21,0,93,217,381,651,0,2667,8191,11811,24573,57337,82677,
%T A247956 172011,393213,761763,1572861,2752491,5332341,11010027,21845397,
%U A247956 48758691,85327221,199753347,341310837,677207307,1398273429,3220807683,6192353757,10836557067
%N A247956 a(n) is the smallest number k such that sigma(k) = 2^n or 0 if no such k exists.
%C A247956 See A078426 for numbers n such that there is no solution to the equation sigma(x) = 2^n.
%C A247956 If a(n) > 0, then it is a term of A046528 (numbers that are a product of distinct Mersenne primes).
%H A247956 Amiram Eldar, <a href="/A247956/b247956.txt">Table of n, a(n) for n = 0..300</a>
%H A247956 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%F A247956 a(A078426(n)) = 0.
%F A247956 a(A182221(n)) > 0.
%e A247956 a(0) = 1 because 1 is the smallest number k with sigma(1) = 1 = 2^0.
%e A247956 a(5) = 21 because 21 is the smallest number k with sigma(k) = 32 = 2^5.
%e A247956 a(6) = 0 because there is no number k with sigma(k) = 64 = 2^6.
%o A247956 (PARI) a(n) = for (k=1, 2^n, if (sigma(k)== 2^n, return (k))); return (0); \\ _Michel Marcus_, Oct 03 2014, Oct 31 2015
%o A247956 (PARI) a(n) = max(0, invsigmaMin(1<<n)); \\ _Amiram Eldar_, Dec 31 2024, using _Max Alekseyev_'s invphi.gp (see links).
%Y A247956 Cf. A000203, A046528, A078426, A180162, A180221, A182221, A295043.
%K A247956 nonn
%O A247956 0,3
%A A247956 _Jaroslav Krizek_, Sep 28 2014
%E A247956 a(0) = 1 prepended by _Michel Marcus_, Oct 31 2015