A070164 Least number m such that cototient(m) - 1 = prime(n).

9, 6, 10, 12, 18, 26, 34, 38, 36, 42, 48, 74, 82, 60, 72, 78, 84, 122, 134, 108, 146, 152, 164, 126, 194, 202, 206, 156, 150, 226, 192, 180, 198, 204, 222, 296, 266, 260, 328, 258, 252, 338, 288, 386, 270, 398, 340, 392, 452, 350, 342, 336, 482, 372, 514, 360

Offset: 1

Author

Labos Elemer, Apr 26 2002

Keywords

• nonn

Examples

			prime(17) = 59, cototient(k) - 1 = 59 for k = 84, 100, 116 and 118, and the smallest is a(17) = 84.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A051953, A070162, A219428.

Programs

Mathematica

seq[lim_] := Module[{c = Table[n - EulerPhi[n] - 1, {n, 1, lim}], m}, m = PrimePi[Max[c]]; TakeWhile[Flatten[FirstPosition[c,#]& /@ Prime[Range[m]]], !MissingQ[#] &]]; seq[600] (* Amiram Eldar, Mar 17 2025 *)

PARI

list(len) = {my(v = vector(len), k = 2, c = 0, p, i); while(c < len, p = k - eulerphi(k) - 1; if(isprime(p), i = primepi(p); if(i <= len && v[i] == 0, v[i] = k; c++)); k++); v;} \\ Amiram Eldar, Mar 17 2025

Formula

a(n) = Min{x: A051953(x) - 1 = n-th prime}.