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A058339
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Number of solutions to 1+Phi[x] = p(n), where p(n) is the n-th prime, phi is A000010.
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1
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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, 2, 2, 12, 5, 4, 2, 2, 2, 4, 2, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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EXAMPLE
| Phi(x)=p-1 always has at least 2 solutions: p and 2p a prime and a composite. Many times more than 2 x gives Phi(x)=p-1. For p-1=96 there are 17(i.e. 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 p-1=100 there are 4(an even number of) solutions:{101, 125, 202, 250}. For all odd solutions x, 2x 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}.
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MAPLE
| with(numtheory): >[seq(nops(invphi(-1+ithprime(i))), i=1..256)];
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CROSSREFS
| Cf. A000010, A000040, A066071-A066080, A006093.
Sequence in context: A174015 A014292 A066078 * A133852 A093150 A167831
Adjacent sequences: A058336 A058337 A058338 * A058340 A058341 A058342
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Dec 14 2000
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