A051961 Smallest number w such that A051953(w) = w - phi(w) is the n-th prime.

4, 9, 25, 15, 35, 33, 65, 51, 95, 161, 87, 217, 185, 123, 215, 329, 371, 177, 427, 335, 213, 511, 395, 581, 1501, 485, 303, 515, 321, 545, 255, 635, 917, 411, 1529, 447, 1057, 1099, 455, 1169, 1211, 537, 1991, 573, 965, 591, 435, 2743, 1115, 681, 665

Offset: 1

Author

Labos Elemer, Jan 05 2000

Keywords

• nonn

Examples

			The 31st term is 255 since 255 - phi(255) = 127, the 31st prime, and no number less than 255 has this property.
		

Links

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

Crossrefs

Cf. A050530, A051953.

Programs

Mathematica

With[{c=Table[n-EulerPhi[n],{n,4000}]},Table[Position[c,p,1,1],{p,Prime[ Range[ 60]]}]]//Flatten (* Harvey P. Dale, Sep 14 2020 *)

PARI

a(n) = {my(k = 1); while(k - eulerphi(k) != prime(n), k++); k;} \\ Michel Marcus, Feb 02 2015

Formula

A050530(a(n)) = prime(n) and a(n) is the least number with this property.

a(n) = A063507(A000040(n)). - Michel Marcus, Feb 02 2015