## Numbers such that concatenation of prime factors is a power

For example,

$10 \; = \; 2 \; \times \: \; 5$
$25 \; = \; 5^2$

$14 \; = \; 2 \; \times \: \; 7$
$27 \; = \; 3^3$

$20 \; = \; 2 \; \times \: \; 2 \; \times \: \; 5$
$225 \; = \; 15^2$

$86 \; = \; 2 \; \times \: \; 43$
$243 \; = \; 3^5$

$129 \; = \; 3 \; \times \: \; 43$
$343 \; = \; 7^3$

$145 \; = \; 5 \; \times \: \; 29$
$529 \; = \; 23^2$

$178 \; = \; 2 \; \times \: \; 89$
$289 \; = \; 17^2$

$183 \; = \; 3 \; \times \: \; 61$
$361 \; = \; 19^2$

$203 \; = \; 7 \; \times \: \; 29$
$729 \; = \; 3^6$

$394 \; = \; 2 \; \times \: \; 197$
$2197 \; = \; 13^3$

$403 \; = \; 13 \; \times \: \; 31$
$1331 \; = \; 11^3$

$802 \; = \; 2 \; \times \: \; 401$
$2401 \; = \; 7^4$

math grad - Interest: Number theory
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### 1 Response to Numbers such that concatenation of prime factors is a power

1. David @InfinitelyManic says:

Repost …

(10,[2,5],25,2)
(14,[2,7],27,3)
(20,[2,5],25,2)
(28,[2,7],27,3)
(40,[2,5],25,2)
(50,[2,5],25,2)
(56,[2,7],27,3)
(80,[2,5],25,2)
(86,[2,43],243,5)
(98,[2,7],27,3)
(100,[2,5],25,2)
(112,[2,7],27,3)
(129,[3,43],343,3)
(145,[5,29],529,2)
(160,[2,5],25,2)
(172,[2,43],243,5)
(178,[2,89],289,2)
(183,[3,61],361,2)
(196,[2,7],27,3)
(200,[2,5],25,2)
(203,[7,29],729,2)
(203,[7,29],729,3)
(203,[7,29],729,6)
(224,[2,7],27,3)
(250,[2,5],25,2)
(320,[2,5],25,2)
(344,[2,43],243,5)
(356,[2,89],289,2)
(387,[3,43],343,3)
(392,[2,7],27,3)
(394,[2,197],2197,3)
(400,[2,5],25,2)
(403,[13,31],1331,3)
(448,[2,7],27,3)
(500,[2,5],25,2)
(549,[3,61],361,2)
(640,[2,5],25,2)
(686,[2,7],27,3)
(688,[2,43],243,5)
(712,[2,89],289,2)
(725,[5,29],529,2)
(784,[2,7],27,3)
(788,[2,197],2197,3)
(800,[2,5],25,2)
(802,[2,401],2401,2)
(802,[2,401],2401,4)
(896,[2,7],27,3)
(1000,[2,5],25,2)