A291503 a(n) is the smallest k such that sigma(k) = phi(n), or 0 if no such k exists.

1, 1, 0, 0, 3, 0, 5, 3, 5, 3, 0, 3, 6, 5, 7, 7, 0, 5, 10, 7, 6, 0, 0, 7, 19, 6, 10, 6, 12, 7, 29, 0, 19, 0, 14, 6, 22, 10, 14, 0, 27, 6, 20, 19, 14, 0, 0, 0, 20, 19, 21, 14, 0, 10, 27, 14, 22, 12, 0, 0, 24, 29, 22, 21, 33, 19, 0, 21, 43, 14, 0, 14, 30, 22, 27, 22, 24, 14, 45

Offset: 1

Author

Altug Alkan, Aug 25 2017

Keywords

• nonn
• easy

Examples

			a(5) = 3 because sigma(3) = phi(5) and 3 is the smallest number with this property.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A051444, A069825.

Programs

Maple

N:= 100: # to get a(1)..a(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:
seq(R[numtheory:-phi(n)],n=1..N); # Robert Israel, Aug 25 2017

PARI

a(n) = for(k=1, eulerphi(n), if(sigma(k)==eulerphi(n), return(k))); 0 \\ after Charles R Greathouse IV at A051444

Formula

a(A069825(n)) = 0 for n > 1.

a(n) = A051444(A000010(n)). - Michel Marcus, Aug 25 2017