A014573 Smallest k such that phi(x) = k has exactly n solutions.

3, 0, 1, 2, 4, 8, 12, 32, 36, 40, 24, 48, 160, 396, 2268, 704, 312, 72, 336, 216, 936, 144, 624, 1056, 1760, 360, 2560, 384, 288, 1320, 3696, 240, 768, 9000, 432, 7128, 4200, 480, 576, 1296, 1200, 15936, 3312, 3072, 3240, 864, 3120, 7344, 3888, 720, 1680

Offset

0,1

Comments

Carmichael conjectured that no term exists for n=1.

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

Links

Table of n, a(n) for n=0..50.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Max Alekseyev, PARI scripts for various problems

Eric Weisstein's World of Mathematics, Carmichael's Totient Function conjecture

Prog

(PARI) a(n) = if (n==1, 0, my(k=1); while (#invphi(k) != n, k++); k); \\ using invphi in PARI scripts link; Michel Marcus, Oct 09 2023

Crossrefs

Cf. A000010. Essentially same as A007374, which is the main entry for this sequence.

Sequence in context: A194801 A361287 A273901 * A067166 A125209 A356517

Adjacent sequences: A014570 A014571 A014572 * A014574 A014575 A014576

Keyword

nonn,easy

Author

Eric W. Weisstein

Extensions

Link fixed by Charles R Greathouse IV, Oct 06 2009

Status

approved