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Search: id:A097061
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| A097061 |
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Carmichael numbers that do not satisfy the rule that every Carmichael number minus one is a Niven/Harshad number. |
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+0
2
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| 561, 63973, 75361, 162401, 278545, 656601, 825265, 838201, 852841, 1050985, 1857241, 1909001, 3224065, 3828001, 4903921, 5444489, 5481451, 5632705, 5968873, 6049681, 6189121, 7995169, 8355841, 8830801, 8927101, 9494101
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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8355841, 8830801, 8927101 are the first three consecutive Carmichael numbers to fail the criterion. Terms checked up to 10^16.
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REFERENCES
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Granville, Andrew and Pomerance, Carl, Two contradictory conjectures concerning Carmichael numbers. Math. Comp. 71 (2002), no. 238, 883-908.
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LINKS
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Rob Hoogers, Complete list of terms UP to 10^16 with all relevant data (5.3MB zipped textfile)
Granville, Andrew and Pomerance, Carl, Two contradictory conjectures concerning Carmichael numbers
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FORMULA
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a(n) = if(sum of digits(n-1))/number of digits<>int(sum of digits(n-1)/number of digits, n, 0)
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EXAMPLE
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Add all digits in 560 to get 11, which gives 560/11<>int(560/11) and continue likewise with 1104/6==int(1104/6), 1728/18==int(1728/18), etc.
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PROGRAM
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(pseudocode) if((n-1)/digitsum(n-1)<>int(n-1)/digitsum(n-1), n, 0)
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CROSSREFS
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Cf. A002997.
Sequence in context: A141706 A083736 A006931 this_sequence A139089 A121508 A135437
Adjacent sequences: A097058 A097059 A097060 this_sequence A097062 A097063 A097064
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KEYWORD
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nonn
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AUTHOR
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Rob Hoogers (chimera(AT)chimera.fol.nl), Jul 21 2004
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 16 2006
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