# [seqfan] Re: sigma(n)+sigma(n+1)+sigma(n+2) = sigma(n+3)

Fri Oct 29 11:57:58 CEST 2021

```I would be very surprised if all examples had n == 7 (mod 10). You might have to go quite high to find a counter-example, however.

In general, one would expect all these to have n+3 highly divisible, but not always divisible by any specified prime.

The examples shown here all n == 7 mod (1260). 1260 = 2^2 * 3^2 * 5 * 7.

Look also at A065900.

-----Original Message-----
From: michel.marcus at free.fr
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Oct 29, 2021 3:10 am
Subject: [seqfan] Re: sigma(n)+sigma(n+1)+sigma(n+2) = sigma(n+3)

If one searches with <= instead of =, one gets 10077, 15117, 20157, 25197, 27717, 37797, 41577, 42837, 45357, ...
Where it appears that terms are 7 (mod 10), s o that n+3 would be 0 (mod 10).

MM

----- Mail original -----

De: "michel marcus" <michel.marcus at free.fr>
À: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Envoyé: Mardi 26 Octobre 2021 09:36:44
Objet: [seqfan] sigma(n)+sigma(n+1)+sigma(n+2) = sigma(n+3)

Hello seqfans

A348335 has term 591357 that satisfies sigma(n)+sigma(n+1)+sigma(n+2) = sigma(n+3).
735205677 has the same property.

Can you get more terms like them ?
Best.
MM

```