

A220847


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


1



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
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OFFSET

1,2


COMMENTS

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


LINKS



FORMULA

a(n) = sum_(dn) (product_(dn) d) / (product_( d_xn , d_x<=d) d_x) = sum_(dn) (A007955(n)) / (product_( d_xn , 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



KEYWORD

nonn


AUTHOR



STATUS

approved



