A014573 Smallest k such that phi(x) = k has exactly n solutions, n>=0 with Carmichael conjecture.

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

Author

Eric W. Weisstein

Keywords

• nonn
• easy

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

• 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/GP Scripts for Miscellaneous Math Problems (invphi.gp).
• Eric Weisstein's World of Mathematics, Carmichael's Totient Function conjecture

Crossrefs

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

Programs

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

Extensions

Link fixed by Charles R Greathouse IV, Oct 06 2009