A069822 - OEIS

A069822

Numbers k for which there is at least one x < k such that sigma(x) = sigma(k).

%I #15 Dec 20 2024 02:36:34

%S 11,15,17,23,25,26,31,35,38,39,41,46,47,51,53,55,56,58,59,62,65,69,70,

%T 71,75,77,78,79,82,83,87,89,92,94,95,97,103,107,110,113,115,116,118,

%U 119,122,123,124,125,127,130,131,135,139,140,141,142,143,145,151,153

%N Numbers k for which there is at least one x < k such that sigma(x) = sigma(k).

%C Numbers k for which A263025(k) > 1. - _Antti Karttunen_, Dec 08 2017

%H Antti Karttunen, <a href="/A069822/b069822.txt">Table of n, a(n) for n = 1..10547</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

%o (PARI) for(s=1,200,if(prod(i=1,s-1, sigma(i)-sigma(s))==0,print1(s,",")))

%o (PARI) for(n=1,16384,y=0;s=sigma(n);for(k=1,(n-1),if(sigma(k)==s,y=1;break)); if(y,i++;write("b069822.txt", i," ", n))); \\ _Antti Karttunen_, Dec 08 2017

%o (PARI) is(k) = invsigmaMin(sigma(k)) < k; \\ _Amiram Eldar_, Dec 20 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A263025, A296214.

%Y Cf. A296087 (a subsequence).

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 28 2002