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%I #40 Oct 06 2021 11:58:54
%S 1,0,3,7,0,21,0,93,217,381,651,0,2667,8191,11811,24573,57337,82677,
%T 172011,393213,761763,1572861,2752491,5332341,11010027,21845397,
%U 48758691,85327221,199753347,341310837,677207307,1398273429,3220807683,6192353757,10836557067
%N a(n) is the smallest number k such that sigma(k) = 2^n or 0 if no such k exists.
%C See A078426 for numbers n such that there is no solution to the equation sigma(x) = 2^n.
%C If a(n) > 0, then it is a term of A046528 (numbers that are a product of distinct Mersenne primes).
%F a(A078426(n)) = 0.
%F a(A182221(n)) > 0.
%e a(0) = 1 because 1 is the smallest number k with sigma(1) = 1 = 2^0.
%e a(5) = 21 because 21 is the smallest number k with sigma(k) = 32 = 2^5.
%e a(6) = 0 because there is no number k with sigma(k) = 64 = 2^6.
%o (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
%Y Cf. A000203, A046528, A078426, A180162, A180221, A295043.
%K nonn
%O 0,3
%A _Jaroslav Krizek_, Sep 28 2014
%E a(0) = 1 prepended by _Michel Marcus_, Oct 31 2015
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