A051445 Smallest k such that phi(k) = 2n, or 0 if there is no such k.

3, 5, 7, 15, 11, 13, 0, 17, 19, 25, 23, 35, 0, 29, 31, 51, 0, 37, 0, 41, 43, 69, 47, 65, 0, 53, 81, 87, 59, 61, 0, 85, 67, 0, 71, 73, 0, 0, 79, 123, 83, 129, 0, 89, 0, 141, 0, 97, 0, 101, 103, 159, 107, 109, 121, 113, 0, 177, 0, 143, 0, 0, 127, 255, 131, 161, 0, 137

Offset: 1

Author

Jud McCranie

Keywords

• nonn

Comments

The zero values are easy to prove because of the bounds on the phi function.

Examples

			a(4) = 15 as phi(15) = 2*4 and no k < 15 has phi(k) = 2*4.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002181, A072075, A079695. For records see A132012, A132115.

Programs

PARI

a(n)=n+=n;for(k=n+1, solve(x=n,if(n<20,99,5*n*log(log(n))), x/(exp(Euler)*log(log(x))+3/log(log(x)))-n), if(eulerphi(k)==n,return(k))); 0 \\ Charles R Greathouse IV, Dec 19 2011

Formula

a(10^n/2) = A072075(n). - R. J. Mathar, Dec 12 2024

a(A079695(n)) = 0. - David A. Corneth, Dec 12 2024