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Search: id:A072513
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| A072513 |
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Product of all n - d, where d < n and d is a divisor of n. |
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+0
6
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| 1, 1, 2, 6, 4, 60, 6, 168, 48, 360, 10, 47520, 12, 1092, 1680, 20160, 16, 440640, 18, 820800, 5040, 4620, 22, 734469120, 480, 7800, 11232, 4953312, 28, 3946320000, 30, 9999360, 21120, 17952, 28560, 439723468800, 36, 25308, 35568, 35852544000
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(n) = (n-d_1)(n-d_2)...(n-d_k) where d_k is the largest divisor of n less than n (k = tau(n) - 1).
a(p) = p-1, a(pq) = pq(p-1)(q-1)(pq-1), p and q prime.
If n is not a prime or a prime square then n divides a(n).
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EXAMPLE
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a(6) = (6-1)(6-2)(6-3) = 60.
For n = 16 the divisors d < n are 1,2,4 and 8, so a(16) = (16-1)*(16-2)*(16-4)*(16-8) = 15*14*12*8 = 20160.
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PROGRAM
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(PARI) for(n=1, 40, d=divisors(n); print1(prod(j=1, matsize(d)[2]-1, n-d[j]), ", "))
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CROSSREFS
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Cf. A072512, A080497, A080498, A080500.
Sequence in context: A108435 A126262 A080499 this_sequence A022404 A118138 A004583
Adjacent sequences: A072510 A072511 A072512 this_sequence A072514 A072515 A072516
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 28 2002
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 31 2002
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