A220847 a(n) = numerator of the fraction whose Engel expansion has the positive divisors of n as its terms.

1, 3, 4, 13, 6, 61, 8, 105, 37, 161, 12, 2965, 14, 309, 316, 1681, 18, 9901, 20, 13221, 610, 749, 24, 569401, 151, 1041, 1000, 36093, 30, 1381981, 32, 53793, 1486, 1769, 1506, 17294509, 38, 2205, 2068, 4232841, 42, 5285869, 44, 139437, 128296, 3221, 48

Offset

1,2

Comments

Conjecture: sequence is injective (all terms of this sequence occur only once).

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..100

Formula

a(n) = sum_(d|n) (product_(d|n) d) / (product_( d_x|n , d_x<=d) d_x) = sum_(d|n) (A007955(n)) / (product_( d_x|n , d_x<=d) d_x).

a(p) = p + 1 for prime p.

Example

The divisors of 6 are 1, 2, 3, 6.
So a(6) is the numerator of 1/1+1/(1*2)+1/(1*2*3)+1/(1*2*3*6)=61/36.
a(6) = 36/1+36/(1*2)+36/(1*2*3)+36/(1*2*3*6)=36+18+6+1=61.

Crossrefs

Cf. A007955 (denominators).

Sequence in context: A242648 A327583 A324159 * A127611 A308688 A324501

Adjacent sequences: A220844 A220845 A220846 * A220848 A220849 A220850

Keyword

nonn

Author

Jaroslav Krizek, Dec 22 2012

Status

approved