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A295043
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a(n) is the largest number k such that sigma(k) = 2^n or 0 if no such k exists.
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1
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1, 0, 3, 7, 0, 31, 0, 127, 217, 381, 889, 0, 3937, 8191, 11811, 27559, 57337, 131071, 253921, 524287, 1040257, 1777447, 4063201, 7281799, 16646017, 32247967, 66584449, 116522119, 225735769, 516026527, 1073602561, 2147483647, 4294434817, 7515217927, 15032385529
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OFFSET
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0,3
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COMMENTS
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If a(n) > 0, then it is a term of A046528 (numbers that are a product of distinct Mersenne primes).
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 1 because 1 is the largest number k with sigma(k) = 1 = 2^0.
a(5) = 31 because 31 is the largest number k with sigma(k) = 32 = 2^5.
a(6) = 0 because there is no number k with sigma(k) = 64 = 2^6.
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PROG
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(PARI) a(n) = {local(r, k); r=0; for(k=1, 2^n, if(sigma(k) == 2^n, r=k)); return(r)}; \\ Michael B. Porter, Nov 14 2017
(PARI) a(n) = forstep(k=2^n, 1, -1, if (sigma(k)==2^n, return (k))); return (0) \\ Rémy Sigrist, Jan 08 2018
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CROSSREFS
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Cf. A247956 (the smallest number k instead of the largest).
Cf. A078426 (no solution to the equation sigma(x)=2^n).
A000668 (Mersenne primes) is a subsequence.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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