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Search: id:A129510
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| A129510 |
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Number of distinct differences between pairs of distinct divisors of n. |
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+0
6
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| 0, 1, 1, 3, 1, 5, 1, 6, 3, 6, 1, 10, 1, 6, 5, 10, 1, 13, 1, 13, 6, 6, 1, 18, 3, 6, 6, 14, 1, 19, 1, 15, 6, 6, 6, 24, 1, 6, 6, 22, 1, 23, 1, 15, 12, 6, 1, 30, 3, 15, 6, 15, 1, 25, 6, 23, 6, 6, 1, 37, 1, 6, 13, 21, 6, 25, 1, 15, 6, 24, 1, 40, 1, 6, 13, 15, 6, 26, 1, 34, 10, 6, 1, 45, 6, 6, 6, 26
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OFFSET
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1,4
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COMMENT
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a(n) = #{|x-y|: x <> y and n mod x = n mod y = 0};
a(n) = 1 iff n is prime;
a(n) <= A000217(A000005(a(n))-1) = A066446(n):
a(A129511(n))=A066446(A129511(n)), a(A129512(n))<A066446(A129512(n)).
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LINKS
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Eric Weisstein's World of Mathematics, Divisor
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EXAMPLE
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n=44, set of divisors of 44 = {1,2,4,11,22,44}:
44-22=22, 44-11=33, 44-4=40, 44-2=42, 44-1=41,
22-11=11, 22-4=18, 22-2=20, 22-1=21,
11-4=7, 11-2=9, 11-1=10, 4-2=2, 4-1=3, 2-1=1,
a(44) = #{1,2,3,7,9,10,11,18,20,21,22,33,40,41,42} = 15;
n=45, set of divisors of 45 = {1,3,5,9,15,45}:
45-15=30, 45-9=36, 45-5=40, 45-3=42, 45-1=44,
15-9=6, 15-5=10, 15-3=12, 15-1=14,
9-5=4, 9-3=6, 9-1=8, 5-3=2, 5-1=4, 3-1=2,
a(45) = #{2,4,6,8,10,12,14,30,36,40,42,44} = 12.
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CROSSREFS
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Cf. A000005.
Sequence in context: A046730 A002972 A029652 this_sequence A087913 A090585 A147661
Adjacent sequences: A129507 A129508 A129509 this_sequence A129511 A129512 A129513
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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), Apr 19 2007
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