A073460 a(n) = smallest solution x to n + pi(x) = phi(x), or 0 if no such solution exists.

30, 6, 2, 1, 7, 26, 21, 11, 13, 180, 46, 17, 19, 25, 39, 23, 64, 74, 174, 51, 29, 31, 57, 104, 94, 228, 37, 69, 116, 41, 43, 258, 65, 47, 81, 87, 134, 99, 53, 280, 146, 77, 135, 59, 61, 111, 166, 172, 184, 67, 91, 408, 71, 73, 194, 129, 202, 780, 79, 212, 115, 83

Offset

-2,1

Comments

Although pi takes all values, solutions are not guaranteed since nontotient numbers exist.

First possible holes (k>10^6) are for n = -3, 63, 73, 144, 162, 185, 204, 228, 233, 256, 264,...

Using phi(x) >= x / (exp(gamma)*log(log(x)) + 2) and pi(x) <= x / log(x) all the holes > 0 are easily proved. - Sean A. Irvine, Nov 29 2024

Links

Sean A. Irvine, Table of n, a(n) for n = -2..10000

Formula

a(n)=Min{x; A000010(x)-A000720(x)=n}

Example

n=13: Phi[13]=12, Pi[13]=6, a[12-6]=a(6)=13; n=63: no solution was found at x<=1000000.

Mathematica

Do[k = 1; While[ EulerPhi[k] != PrimePi[k] + n, k++ ]; Print[k], {n, -2, 62}]

Crossrefs

Cf. A000010, A000720, A037228, A037171, A073453-A073457, A072530, A072531, A073461, A073462.

Sequence in context: A299195 A040878 A328962 * A036390 A040879 A040877

Adjacent sequences: A073457 A073458 A073459 * A073461 A073462 A073463

Keyword

nonn

Author

Labos Elemer, Aug 02 2002

Extensions

Edited by Robert G. Wilson v, Aug 12 2002

Status

approved