login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A014573
Smallest k such that phi(x) = k has exactly n solutions.
8
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
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].
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
KEYWORD
nonn,easy
EXTENSIONS
Link fixed by Charles R Greathouse IV, Oct 06 2009
STATUS
approved