A072296 Least number starting a chain of exactly n consecutive even integers that do not have cototient-inverses.

10, 50, 532, 2314, 4628, 22578, 115024, 221960, 478302, 3340304, 22527850, 117335136, 1118736102, 1564578508, 6121287812, 7515991946

Offset: 1

Author

Robert G. Wilson v, Jul 12 2002

Keywords

• hard
• more
• nonn

Comments

If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*q-phi(p*q)=p+q-1 and then every odd number can be expressed as x-phi(x). - Benoit Cloitre, Mar 03 2002.

Examples

			Neither 50 nor 52 have cototient-inverses and since 50 is the first of the two and the least number with this property, a(2) = 50.
		

Crossrefs

Cf. A005278, A051953, A063512, A063740.

Programs

Mathematica

a = Table[0, {5*10^7}]; Do[b = n - EulerPhi[n]; If[ b < 5*10^7 + 1, a[[b/2]]++ ], {n, 2, 615437100}] (* used to find a(7) *) Do[ If[ a[[n]] == a[[n + 1]] == a[[n + 2]] == a[[n + 3]] == a[[n + 4]] == a[[n + 5]] == a[[n + 6]] == 0, Print[n]], {n, 1, 10^6}]

Extensions

a(12)-a(14) from Donovan Johnson, Jun 23 2010

a(15)-a(16) from Donovan Johnson, Jun 03 2013