## Num3er 2016 – sum of all the divisors

$\sigma_1 \, (N)$   is the sum of all the divisors of   $N$

$\sigma_1 \, (672) \; = \; 2016 \; = \; 3 \; \times \; 672$

Find other values for   N   for which   $\sigma_1 \, (N) \; = \; 3 \, N$

Numbers of the form   $2^n \; \times \; 3 \; \times \; p$   may satisfy the condition

n = 3   —>   $120 \; = \; 2^3 \times 3 \times 5$
$\sigma_1 \, (120) \; = \; 360 \; = \; 3 \; \times \; 672$

n = 4   —>   ….

n = 5   —>   $672 \; = \; 2^5 \times 3 \times 7$
$\sigma_1 \, (672) \; = \; 2016 \; = \; 3 \; \times \; 672$

n = 6   —>   ….

n = 7   —>   ….

n = 8   —>   $459818240 \; = \; 2^8 \times 5 \times 7 \times 19 \times 37 \times 73$
$\sigma_1 \, (459818240) \; = \; 1379454720 \; = \; 3 \; \times \; 459818240$

n = 9   —>   $523776 \; = \; 2^9 \times 3 \times 11 \times 31$
$\sigma_1 \, (523776) \; = \; 1571328 \; = \; 3 \; \times \; 523776$

n = 10   —>   ….

n = 11   —>   ….

n = 12   —>   ….

n = 13   —>   $1476304896 \; = \; 2^{13} \times 3 \times 11 \times 43 \times 127$
$\sigma_1 \, (1476304896) \; = \; 4428914688 \; = \; 3 \; \times \; 1476304896$

n = 14   —>   $51001180160 \; = \; 2^{14} \times 5 \times 7 \times 19 \times 31 \times 151$
$\sigma_1 \, (51001180160) \; = \; 153003540480 \; = \; 3 \; \times \; 51001180160$

n = 15   —>   ….

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math grad - Interest: Number theory
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### 2 Responses to Num3er 2016 – sum of all the divisors

1. paul says:

Here are 2 more

d(120) = 360 = 3 x 120
d(523776) = 1571328 = 3 x 523776

Paul

• benvitalis says:

Nice! Please check out my post and see whether you can find solutions I put blanl