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A020491
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Numbers n such that sigma_0(n) divides phi(n).
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3
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1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 26, 28, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 82, 83, 84, 85, 87, 88, 89, 90, 91, 93, 95, 97, 98, 99, 101, 102, 103, 104
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| In other words, numbers n such that d(n) divides phi(n).
Contribution from Enrique Pérez Herrero, Aug 11 2010: (Start)
sigma_0(n) divides phi(n) when:
n is an odd prime: A065091
n is an odd squarefree number: A056911
2^m, where m is a Mersenne number: A000225
if d divides (p-1), with p a prime, then p^(d-1) is in this sequence.
and also p^(p-1), p^(p-2) and p^(-1+p^n).
(End)
phi(n) and d(n) are multiplicative functions so, if m and n are coprime and both of them are in this sequence then m*n is also in this sequence. [Enrique Pérez Herrero, Sep 05 2010]
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LINKS
| Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
Psychedelic Geometry Blogspot-Fermat and Mersenne Numbers Conjecture-(2) [From Enrique Pérez Herrero, Aug 11 2010]
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MATHEMATICA
| Select[ Range[ 105 ], IntegerQ[ EulerPhi[ # ]/DivisorSigma[ 0, # ] ]& ]
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CROSSREFS
| Cf. A000005, A000010.
Cf. A015733 [From Enrique Pérez Herrero, Aug 11 2010]
Complement of A015733 [From Enrique Pérez Herrero, Aug 11 2010]
Sequence in context: A131903 A141114 A136443 * A168501 A173186 A047746
Adjacent sequences: A020488 A020489 A020490 * A020492 A020493 A020494
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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