A070162 -id:A070162 - cp's OEIS frontend

A070163 Primes arising in A070162.

3, 3, 2, 5, 7, 7, 7, 11, 11, 11, 13, 17, 23, 19, 23, 29, 23, 23, 31, 29, 31, 29, 43, 31, 31, 47, 37, 53, 47, 41, 59, 43, 47, 47, 47, 59, 53, 71, 59, 59, 61, 89, 67, 71, 71, 73, 109, 79, 107, 79, 107, 83, 83, 89, 131, 109, 127, 97, 137, 101, 139, 103, 107, 107, 109, 139

Offset: 1

Labos Elemer, Apr 26 2002

nonn

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

Cf. A000010, A051953, A070162.

Do[s=n-EulerPhi[n]-1; If[PrimeQ[s], Print[s]], n, 1, 10000]

lista(kmax) = {my(p); for(k = 1, kmax, p = k - eulerphi(k) - 1; if(isprime(p), print1(p, ", ")));} \\ Amiram Eldar, Nov 07 2024

a(n) = A070162(n) - A000010(A070162(n)) - 1 = A051953(A070162(n)) - 1.

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

Original entry on oeis.org

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

Labos Elemer, Apr 26 2002

nonn

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

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

Cf. A000010, A051953, A070162, A219428.

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 *)

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

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

cp's OEIS Frontend

A070163 Primes arising in A070162.

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