

A058339


Number of solutions to 1 + phi(x) = prime(n), where phi is A000010.


9



2, 3, 4, 4, 2, 6, 6, 4, 2, 2, 2, 8, 9, 4, 2, 2, 2, 9, 2, 2, 17, 2, 2, 6, 17, 4, 2, 2, 9, 6, 2, 2, 2, 2, 2, 2, 7, 4, 2, 2, 2, 10, 2, 21, 2, 2, 2, 2, 2, 2, 6, 2, 31, 2, 10, 2, 2, 2, 9, 8, 2, 2, 2, 2, 16, 2, 2, 18, 2, 6, 12, 2, 2, 2, 2, 2, 2, 13, 13, 6, 2, 13, 2, 34
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OFFSET

1,1


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
D. Bressoud, CNT.m Computational Number Theory Mathematica package.


FORMULA

a(n) = A210500(n) + A210501(n).  Arkadiusz Wesolowski, Jan 19 2013


EXAMPLE

The equation phi(x) = p1 always has at least 2 solutions: p and 2p a prime and a composite. Many times more than 2 x gives phi(x) = p1. For p1 = 96 there are 17 (that is, an odd number of) solutions: {97, 119, 153, 194, 195, 208, 224, 238, 260, 280, 288, 306, 312, 336, 360, 390, 420}, 4 odd and 13 even numbers while for p1 = 100 there are 4 (an even number of) solutions: {101, 125, 202, 250}. For all odd solutions x, 2x is also a solution.
1+phi(x) = 11 has 2 solutions: 11 and 22; 1+phi(x) = 241 has 31 solutions: x = {241, 287, 305, 325, 369, 385, 429, 465, 482, 488, 495, 496, 525, 572, 574, 610, 616, 620, 650, 700, 732, 738, 744, 770, 792, 858, 900, 924, 930, 990, 1050}.


MAPLE

with(numtheory): >[seq(nops(invphi(1+ithprime(i))), i=1..256)];


MATHEMATICA

Needs["CNT`"]; Table[Length[PhiInverse[Prime[n]  1]], {n, 100}] (* T. D. Noe, Dec 11 2013 *)
Take[Length /@ Values@ KeySelect[KeyMap[# + 1 &, PositionIndex@ Array[EulerPhi, 10^4]], PrimeQ], 84] (* Michael De Vlieger, Dec 29 2017 *)


CROSSREFS

Cf. A000010, A000040, A006093, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080.
Sequence in context: A014292 A244445 A066078 * A133852 A093150 A301297
Adjacent sequences: A058336 A058337 A058338 * A058340 A058341 A058342


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 14 2000


EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Jan 19 2013


STATUS

approved



