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Search: id:A161670
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| A161670 |
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Sum of largest prime factor of composite(k) for k from smallest prime factor of composite(n) to largest prime factor of composite(n). |
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| 3, 5, 3, 2, 13, 5, 23, 10, 3, 5, 13, 20, 38, 5, 5, 56, 2, 23, 13, 3, 35, 80, 15, 5, 92, 53, 13, 23, 38, 10, 129, 5, 7, 13, 77, 56, 5, 30, 23, 89, 187, 13, 215, 20, 3, 48, 38, 80, 126, 23, 5, 263, 10, 92, 22, 56, 13, 2, 329, 23, 72, 365, 184, 38, 13, 40, 129, 212, 398, 84, 5, 23, 35
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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"composite(n)" stands for "n-th composite number", so composite(1) to composite(8) are 4, 6, 8, 9, 10, 12, 14, 15.
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EXAMPLE
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composite(1) = 4; (smallest prime factor of 4) = (largest prime factor of 4) = 2. composite(2) = 6, (largest prime factor of 6) = 3. Hence a(1) = 3.
composite(5) = 10; (smallest prime factor of 10) = 2, (largest prime factor of 10) = 5. composite(2) to composite(5) are 6, 8, 9, 10, largest prime factors are 3, 2, 3, 5. Hence a(5) = 3+2+3+5 = 13.
composite(7) = 14; (smallest prime factor of 14) = 2, (largest prime factor of 14) = 7. composite(2) to composite(7) are 6, 8, 9, 10, 12, 14, largest prime factors are 3, 2, 3, 5, 3, 7. Hence a(5) = 3+2+3+5+3+7 = 23.
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PROGRAM
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(MAGMA) Composites:=[ j: j in [4..100] | not IsPrime(j) ];
[ &+[ E[ #E] where E is PrimeDivisors(Composites[k]): k in [D[1]..D[ #D]] where D is PrimeDivisors(Composites[n]) ]: n in [1..73] ]; [From Klaus Brockhaus, Jun 25 2009]
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CROSSREFS
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Cf. A002808 (composite numbers), A111426 (difference between largest and smallest prime factor of composite(n)).
Sequence in context: A085849 A100481 A101778 this_sequence A135514 A092553 A112755
Adjacent sequences: A161667 A161668 A161669 this_sequence A161671 A161672 A161673
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 16 2009, Jun 18 2009
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EXTENSIONS
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Edited, corrected (a(39)=33 replaced by 23, a(40)=84 replaced by 89) and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 25 2009
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