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

1, 3, 4, 6, 11, 17, 22, 23, 32, 34, 40, 46, 47, 48, 53, 59, 60, 67, 71, 83, 85, 89, 94, 101, 106, 107, 115, 118, 125, 128, 131, 134, 136, 137, 141, 142, 149, 160, 166, 167, 170, 173, 177, 178, 179, 184, 188, 191, 192, 197, 202, 204, 214, 227, 230, 233, 235, 236

Offset: 1

Author

Benoit Cloitre, Apr 28 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010 (phi), A000203 (sigma).

Programs

Maple

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
# Alternative:
N:= 1000: # to get terms <= N
R:= Vector(N):
for k from 1 to N-1 do
  s:= numtheory:-sigma(k);
  if s <= N and R[s] = 0 then R[s]:= k fi;
od:
1, op(select(t -> R[numtheory:-phi(t)]=0, [$2..N])); # Robert Israel, Aug 25 2017

Mathematica

okQ[n_] := NoneTrue[Range[n-1], DivisorSigma[1,#] == EulerPhi[n]&];
Select[Range[250], okQ] (* Jean-François Alcover, Jun 03 2019 *)

PARI

for(n=1,600,if(abs(prod(i=1,n-1,eulerphi(n)-sigma(i)))>0,print1(n,",")))

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).