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Search: id:A145832
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| A145832 |
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Numbers n such that for each divisor d of n, d + n/d is "round" ( "square-root smooth"). |
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3
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| 3, 7, 11, 15, 17, 23, 29, 31, 35, 39, 47, 53, 55, 59, 63, 71, 79, 83, 89, 95, 97, 107, 111, 119, 125, 127, 131, 139, 143, 146, 149, 159, 161, 164, 167, 175, 179, 181, 191, 197, 199, 207, 209, 215, 223, 233, 239, 241, 251, 263, 269, 279, 287, 293, 299, 305, 307
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A necessary condition is that the number be one less than a round number; if this number is prime it's in the sequence.
Even composites in this sequence seem rare (see examples below for more details).
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LINKS
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Eric Weisstein, Round Number
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EXAMPLE
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The first term is a prime one less than the round number 4.
The first composite number in this sequence is 15, with divisor-pair sum 3+5 = 8.
Another such composite is 63, with divisor-pair sums: 3+21 = 24, 7+9 = 16.
There are only five even composites among the first 100 terms of this sequence.
The first such is 146, with divisor-pair sum 2+73 = 75. The second is 164, with divisor-pair sums 2+82 = 84 and 4+41 = 45. The remaining three are 458, 524 and 584.
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PROGRAM
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(MAGMA) [ n: n in [1..310] | forall{ k: k in [ Integers()!(d+n/d): d in [ D[j]: j in [1..a] ] ] | k ge (IsEmpty(T) select 1 else Max(T) where T is [ x[1]: x in Factorization(k) ])^2 } where a is IsOdd(#D) select (#D+1)/2 else #D/2 where D is Divisors(n) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 24 2008]
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CROSSREFS
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Cf. A004809, A080715
Sequence in context: A059568 A003512 A079710 this_sequence A124981 A059554 A103543
Adjacent sequences: A145829 A145830 A145831 this_sequence A145833 A145834 A145835
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KEYWORD
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nonn
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AUTHOR
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Dan Sonnenschein (dans(AT)portal.ca), Oct 20 2008
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