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Search: id:A066446
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| A066446 |
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Number of unordered divisor pairs of n. |
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+0
5
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| 0, 1, 1, 3, 1, 6, 1, 6, 3, 6, 1, 15, 1, 6, 6, 10, 1, 15, 1, 15, 6, 6, 1, 28, 3, 6, 6, 15, 1, 28, 1, 15, 6, 6, 6, 36, 1, 6, 6, 28, 1, 28, 1, 15, 15, 6, 1, 45, 3, 15, 6, 15, 1, 28, 6, 28, 6, 6, 1, 66, 1, 6, 15, 21, 6, 28, 1, 15, 6, 28, 1, 66, 1, 6, 15, 15, 6, 28, 1, 45, 10, 6, 1, 66, 6, 6, 6, 28
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OFFSET
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1,4
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COMMENT
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a(n) = 1 iff n is a prime.
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FORMULA
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Combinations of d(n), the number of divisors of n (A000005), taken two at a time. If the canonical factorization of n into prime powers is Product p^e(p) then d(n) = Product (e(p) + 1). Therefore C( d(n), 2) = d(n)*{ d(n)-1 }/2 which is a triangular number (A000217).
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EXAMPLE
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The divisors of 6 are 1, 2, 3 & 6. In unordered pairs they are {1, 2}, {1, 3}, {1, 6}, {2, 3}, {2, 6}, & {3, 6}. Since there are six pairs, a(6) = 6. Also d(6) = 4. 4*3/2 = 6.
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MATHEMATICA
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Table[ Binomial[ DivisorSigma[0, n], 2], {n, 1, 100}]
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CROSSREFS
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Cf. A000005, A000217, A129510.
Sequence in context: A068436 A019570 A040011 this_sequence A069625 A111614 A076889
Adjacent sequences: A066443 A066444 A066445 this_sequence A066447 A066448 A066449
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 28 2001
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