cp's OEIS Frontend

A069825 Numbers k such that there is no x < k such that sigma(x) = phi(k).

%I A069825 #25 May 04 2025 02:03:54
%S A069825 1,3,4,6,11,17,22,23,32,34,40,46,47,48,53,59,60,67,71,83,85,89,94,101,
%T A069825 106,107,115,118,125,128,131,134,136,137,141,142,149,160,166,167,170,
%U A069825 173,177,178,179,184,188,191,192,197,202,204,214,227,230,233,235,236
%N A069825 Numbers k such that there is no x < k such that sigma(x) = phi(k).
%H A069825 Amiram Eldar, <a href="/A069825/b069825.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert Israel)
%H A069825 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%p A069825 with(numtheory): A069825 := proc(n) local p,i; p := phi(n); for i from 1 to n-1 do if sigma(i) = p then RETURN(NULL) fi od; n end; # _Peter Luschny_, Nov 02 2010
%p A069825 # Alternative:
%p A069825 N:= 1000: # to get terms <= N
%p A069825 R:= Vector(N):
%p A069825 for k from 1 to N-1 do
%p A069825   s:= numtheory:-sigma(k);
%p A069825   if s <= N and R[s] = 0 then R[s]:= k fi;
%p A069825 od:
%p A069825 1, op(select(t -> R[numtheory:-phi(t)]=0, [$2..N])); # _Robert Israel_, Aug 25 2017
%t A069825 okQ[n_] := NoneTrue[Range[n-1], DivisorSigma[1,#] == EulerPhi[n]&];
%t A069825 Select[Range[250], okQ] (* _Jean-François Alcover_, Jun 03 2019 *)
%o A069825 (PARI) for(n=1,600,if(abs(prod(i=1,n-1,eulerphi(n)-sigma(i)))>0,print1(n,",")))
%o A069825 (PARI) isok(k) = {my(p = eulerphi(k), v = invsigma(p)); #v == 0 || vecmin(v) >= k;}; \\ _Amiram Eldar_, May 03 2025, using _Max Alekseyev_'s invphi.gp (see links).
%Y A069825 Cf. A000010 (phi), A000203 (sigma).
%K A069825 easy,nonn
%O A069825 1,2
%A A069825 _Benoit Cloitre_, Apr 28 2002