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Search: id:A084190
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| A084190 |
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a(n) = LeastCommonMultiple{d-1: d>1 and d divides n}. |
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+0
2
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| 1, 1, 2, 3, 4, 10, 6, 21, 8, 36, 10, 330, 12, 78, 28, 105, 16, 680, 18, 684, 60, 210, 22, 53130, 24, 300, 104, 702, 28, 36540, 30, 3255, 160, 528, 204, 157080, 36, 666, 228, 62244, 40, 31980, 42, 9030, 61, 6, 990, 46, 2497110, 48, 3528, 400, 5100, 52, 468520
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Considering the set of divisors>1 of n reduced by 1, a(n) is the smallest number whose divisors contain this set;
a(n)<n iff n=p^k, p prime and 1<=k<=2: a(A001248(n))<A001248(n), a(A000430(n))<A000430(n), a(A080257(n))>A080257(n);
a(n) is odd iff n=2^k.
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EXAMPLE
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n=35: divisors>1 of 35 = {5,7,35}, a(35) = LCM(5-1,7-1,35-1) =
LCM(4,6,34) = 204;
n=36: divisors>1 of 36 = {2,3,4,6,9,12,18,36}, a(36) =
LCM(1-1,3-1,4-1,6-1,9-1,12-1,18-1,36-1) = LCM(1,2,3,5,8,11,17,35) = 1570800.
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CROSSREFS
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Cf. A084191(n)=a(a(n)), A007955.
Sequence in context: A065634 A087548 A111619 this_sequence A088303 A054930 A119798
Adjacent sequences: A084187 A084188 A084189 this_sequence A084191 A084192 A084193
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 18 2003
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