# [seqfan] A conjeture about 34155

Claudio Meller claudiomeller at gmail.com
Sat Apr 14 20:05:09 CEST 2012

```Hi seqfans, one of my blog readers, Jordi Domènech i Arnau, has sent me
this :

*I have looked for the numbers that are equal to the sum of their proper
> divisors, greater than their square root. *

*I found a lot of even numbers with this property, but  I´ve only found
>  one odd number, 34155, with this property.*

He makes the conjeture that 34155 is the only odd number with this
caracteristic.

34155 = 207+253+297+345+495+621+759+1035+1265+1485+2277+3105+3795+6831+11385

I ´ve made the sequence (not in the OEIS):
Numbers N  equal to the sum of its proper divisors greater than sqr (N)

42, 54, 66, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 354, 366,
402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 762, 786, 812,
822, 834, 868, 894, 906, 942, 978, 1002, 1036, 1038, 1074, 1086, 1146,
1148, 1158, 1182, 1194, 1204, 1266, 1316, 1338, 1362, 1372, 1374, 1398,
1434, 1446, 1484, 1506, 1542, 1578, 1614, 1626, 1652, 1662, 1686, 1698,
1708, 1758, 1842, 1866, 1876, 1878, 1902, 1986, 1988, 2022, 2044, 2082,
2094, 2118, 2154, 2202, 2212, 2238, 2274, 2298, 2324, 2334, 2382, 2406,
2454, 2492, 2514, 2526, 2586, 2598, 2634, 2658, 2694, 2716, 2742, 2766,
2778, 2802, 2828, 2874, 2884, 2922, 2946, 2994, 2996, 3018, 3052, 3054,
3126, 3138, 3164, 3246, 3282, 3342, 3378, 3414, 3426, 3462

This sequence has to many terms of  A141545 (Numbers n whose abundance is
12)

Can anybody prove this or find a counterexample?
Do you find this interesting?

Thanks
--
Claudio Meller
http://grageasdefarmacia.blogspot.com
http://todoanagramas.blogspot.com/
http://simplementenumeros.blogspot.com/

```