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Search: id:A067350
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| A067350 |
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Numbers n such that sigma(n)+phi(n) has exactly 4 divisors. |
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+0
3
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| 3, 5, 6, 7, 10, 11, 13, 16, 17, 19, 22, 23, 25, 27, 29, 31, 37, 40, 41, 43, 46, 47, 52, 53, 58, 59, 61, 64, 67, 68, 71, 72, 73, 79, 80, 82, 83, 89, 97, 98, 101, 103, 106, 107, 109, 113, 117, 127, 128, 131, 136, 137, 139, 144, 149, 151, 157, 162, 163, 166, 167, 169
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For all terms up to 10^12, sigma(n)+phi(n) is a product of 2 distinct primes. The only other possibility is that sigma(n)+phi(n) is a cube of a prime, for some n which is either a square or twice a square; does this occur? If not, then this sequence is contained in A067351.
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FORMULA
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A000005(A000010(n)+A000203(n))=4=A067349(n)
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EXAMPLE
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Includes all odd primes and some composites; e.g. 22 and 25, since sigma(22)+phi(22)=36+10=46=2*23 and sigma(25)+phi(25)=31+20=51=3*17.
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MATHEMATICA
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Select[ Range[ 1, 200 ], DivisorSigma[ 0, DivisorSigma[ 1, # ]+EulerPhi[ # ] ]==4& ]
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CROSSREFS
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Cf. A000005, A000010, A000203, A067349, A067351.
Sequence in context: A136806 A073803 A067351 this_sequence A028727 A028762 A047328
Adjacent sequences: A067347 A067348 A067349 this_sequence A067351 A067352 A067353
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 17 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 20 2002
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