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A072296 Least number starting a chain of exactly n consecutive even integers that do not have cototient-inverses. 0
10, 50, 532, 2314, 4628, 22578, 115024, 221960, 478302, 3340304, 22527850, 117335136, 1118736102, 1564578508, 6121287812, 7515991946 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

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.

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}]

CROSSREFS

Cf. A005278, A051953, A063512, A063740.

Sequence in context: A240534 A223161 A216156 * A143558 A106041 A264044

Adjacent sequences:  A072293 A072294 A072295 * A072297 A072298 A072299

KEYWORD

hard,more,nonn

AUTHOR

Robert G. Wilson v, Jul 12 2002

EXTENSIONS

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

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

STATUS

approved

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Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)