A306649 a(n) = numerator of Sum_{d|n} (d/sigma(d)) where sigma(k) = the sum of the divisors of k (A000203).

1, 5, 7, 47, 11, 35, 15, 97, 127, 55, 23, 47, 27, 25, 77, 3567, 35, 635, 39, 517, 105, 115, 47, 97, 491, 45, 1621, 235, 59, 385, 63, 37063, 161, 175, 55, 5969, 75, 13, 27, 1067, 83, 175, 87, 1081, 1397, 235, 95, 3567, 1247, 2455, 245, 423, 107, 1621, 253, 291

Offset

1,2

Comments

Sum_{d|n} (d/sigma(d)) >= 1 for all n >= 1.

Links

Table of n, a(n) for n=1..56.

Formula

a(p) = 2p + 1 for p = odd primes.

Example

Sum_{d|n} (d/sigma(d)) for n >= 1: 1, 5/3, 7/4, 47/21, 11/6, 35/12, 15/8, 97/35, 127/52, 55/18, 23/12, 47/12, 27/14, ...
For n=4; Sum_{d|4} (d/sigma(d)) = 1/sigma(1) + 2/sigma(2) + 4/sigma(4) = 1/1 + 2/3 + 4/7 = 47/21; a(4) = 47.

Prog

(Magma) [Numerator(&+[d / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, d/sigma(d))); \\ Michel Marcus, Mar 03 2019

Crossrefs

Cf. A000203, A306650 (denominators).

Sequence in context: A066219 A278618 A174267 * A075830 A058313 A120301

Adjacent sequences: A306646 A306647 A306648 * A306650 A306651 A306652

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 03 2019

Status

approved