A227927 Numbers n such that phi(sigma(k))/sigma(phi(k)) < phi(sigma(n))/sigma(phi(n)) for all k < n and n is the smallest positive integer with this property.

1, 2, 36, 144, 576, 3600, 14400, 921600, 1040400, 4161600, 8643600, 34574400, 266342400, 700131600, 2800526400, 179233689600, 202338032400, 809352129600

Offset: 1

Author

Vladimir Letsko, Oct 09 2013

Keywords

• nonn

Comments

All known terms excluding a(2) are perfect squares.

Examples

			36 is in the sequence because phi(sigma(36))/sigma(phi(36)) = 18/7 and for all k < 36 phi(sigma(k))/sigma(phi(k)) < 18/7.
		

Crossrefs

Cf. A227011, A062401, A062402, A033632, A229238.

Programs

Maple

s:= n -> numtheory:-phi(numtheory:-sigma(n))/numtheory:-sigma(numtheory:-phi(n)):
  a,na,A[1],sA[1]:=1,1,1,1:
1;for i from 2 do ss:=s(i): if ss>a then na:=na+1:A[na]:=ss:a:=ss:sA[na]:=i:print(sA[na]) fi od: