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A110179 Least k such that phi(n+k)=2*phi(n), where phi is Euler's totient function. 3
2, 1, 2, 1, 10, 2, 6, 7, 4, 5, 14, 3, 22, 7, 2, 1, 34, 3, 18, 12, 14, 3, 46, 8, 16, 9, 10, 7, 58, 2, 30, 19, 8, 17, 30, 3, 36, 19, 26, 11, 82, 3, 86, 11, 20, 23, 94, 3, 80, 5, 34, 13, 106, 3, 68, 9, 16, 29, 118, 4, 82, 15, 10, 21, 32, 9, 94, 17, 20, 34, 142, 32, 112, 17, 48, 15, 66, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Makowski shows that a k exists for each n. It appears that k<=2n. For prime n, it appears that n-1<=k<=2n.

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, 3rd Ed., New York, Springer-Verlag, 2004, Section B36.

Andrzej Makowski, On the equation phi(n+k)=2*phi(n), Elem. Math., 29 (1974), 13.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000

MATHEMATICA

Table[k=1; e=EulerPhi[n]; While[EulerPhi[n+k] != 2e, k++ ]; k, {n, 100}]

CROSSREFS

Cf. A050473 (least k such that phi(n+k)=2*phi(k)).

Sequence in context: A062347 A124781 A124151 * A071559 A071560 A248516

Adjacent sequences:  A110176 A110177 A110178 * A110180 A110181 A110182

KEYWORD

nonn

AUTHOR

T. D. Noe, Jul 15 2005

STATUS

approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)