A066080 Largest solution x to phi(x) + 1 = prime(n).
2, 6, 12, 18, 22, 42, 60, 54, 46, 58, 62, 126, 150, 98, 94, 106, 118, 198, 134, 142, 270, 158, 166, 276, 420, 250, 206, 214, 378, 348, 254, 262, 274, 278, 298, 302, 474, 486, 334, 346, 358, 594, 382, 840, 394, 398, 422, 446, 454, 458, 708, 478, 1050, 502, 1020
Offset: 1
Keywords
Examples
For p = 97: x = {97, 119, 153, 194, 195, 208, 224, 238, 260, 280, 288, 306, 312, 336, 360, 390, 420} is the set of 17 solutions such that phi(x) + 1 = 97.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
- Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
- David M. Bressoud, A Course in Computational Number Theory (webpage), CNT.m, Computational Number Theory Mathematica package.
Programs
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Mathematica
Table[Do[s=1+EulerPhi[n]; If[Equal[s, Prime[k]], Print[{n, s}]], {n, 1, 4*Prime[k]^2}], {k, 1, 100}] Needs["CNT`"]; Table[Solve[EulerPhi[x] == Prime[n] - 1, x][[-1, -1, -1]], {n, 100}] (* T. D. Noe, Nov 07 2011 *) -
PARI
a(n) = invphiMax(prime(n)-1); \\ Amiram Eldar, Dec 16 2024, using Max Alekseyev's invphi.gp