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Search: id:A066031
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| A066031 |
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Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes. |
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+0
3
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| 30, 60, 70, 84, 90, 105, 120, 140, 150, 168, 180, 231, 234, 240, 252, 260, 270, 280, 286, 300, 315, 336, 350, 360, 450, 456, 468, 480, 490, 504, 520, 525, 528, 532, 540, 560, 572, 588, 600, 627, 646, 672, 693, 700, 702, 720, 735, 750, 756, 805, 810, 897
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OFFSET
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1,1
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COMMENT
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Primes and powers of primes have been excluded from the sequence because they trivially satisfy the condition "the sum of the prime factors of n divides n". Call a term of the sequence "primitive" if it is not a multiple of some previous term; for example, 70 is primitive while 60 is not. Are there infinitely many primitive terms? See A064623.
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LINKS
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Pe, J., The Prime-perfect Numbers
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EXAMPLE
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The sum of the prime factors of 70 is 2 + 5 + 7 = 14, which divides 70.
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MATHEMATICA
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Select[ Range[2, 900], IntegerQ[ # / Apply[ Plus, First[ Transpose[ FactorInteger[ # ]]]]] && Mod[ #, # - EulerPhi[ # ]] != 0 & ]
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CROSSREFS
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Sequence in context: A040870 A051488 A051283 this_sequence A071140 A074915 A056954
Adjacent sequences: A066028 A066029 A066030 this_sequence A066032 A066033 A066034
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 12 2001
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 12 2001
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