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

1, 0, 3, 7, 0, 21, 0, 93, 217, 381, 651, 0, 2667, 8191, 11811, 24573, 57337, 82677, 172011, 393213, 761763, 1572861, 2752491, 5332341, 11010027, 21845397, 48758691, 85327221, 199753347, 341310837, 677207307, 1398273429, 3220807683, 6192353757, 10836557067

Offset

0,3

Comments

See A078426 for numbers n such that there is no solution to the equation sigma(x) = 2^n.

If a(n) > 0, then it is a term of A046528 (numbers that are a product of distinct Mersenne primes).

Links

Table of n, a(n) for n=0..34.

Formula

a(A078426(n)) = 0.

a(A182221(n)) > 0.

Example

a(0) = 1 because 1 is the smallest number k with sigma(1) = 1 = 2^0.
a(5) = 21 because 21 is the smallest number k with sigma(k) = 32 = 2^5.
a(6) = 0 because there is no number k with sigma(k) = 64 = 2^6.

Prog

(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

Crossrefs

Cf. A000203, A046528, A078426, A180162, A180221, A295043.

Sequence in context: A199068 A198490 A354797 * A295043 A074051 A335918

Adjacent sequences: A247953 A247954 A247955 * A247957 A247958 A247959

Keyword

nonn

Author

Jaroslav Krizek, Sep 28 2014

Extensions

a(0) = 1 prepended by Michel Marcus, Oct 31 2015

Status

approved