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A093493
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Define the total divisor symmetry of a number n to be the number of values r takes such that n-r and n+r have the same number of divisors. Sequence contains the total divisor symmetry of n.
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2
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0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 3, 4, 2, 3, 5, 5, 5, 7, 2, 6, 6, 6, 5, 11, 6, 6, 9, 7, 4, 12, 5, 10, 10, 7, 10, 16, 6, 8, 11, 11, 8, 17, 8, 10, 15, 10, 10, 20, 6, 14, 13, 13, 9, 21, 12, 18, 13, 13, 11, 29, 7, 12, 20, 16, 14, 21, 13, 14, 13, 16, 18, 33, 13, 16, 23, 16, 16, 28, 13, 24, 20, 15, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Number of partitions of 2n in two parts with equal number divisors. Conjecture: (1) No term is zero for n > 3. (2) Every number k appears finitely many times in the sequence. i.e. for every k there exists a number f(k) so that for all n > f(k), a(n) > k. Subsidiary sequences:(1) The frequency of n. (2 The greatest number m so that a(m) = n.
Does every nonnegative integer occur in this sequence? - Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 12 2006
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EXAMPLE
| a(15) = 5 and the values r takes are 2,3,4,7 and 8 giving the number pairs (13,17), (12,18),(11,19), (8,22) and (7,23) with same number of divisors.
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CROSSREFS
| Cf. A093488, A093491, A093492, A093494.
Sequence in context: A029110 A103959 A035375 * A087162 A046925 A090529
Adjacent sequences: A093490 A093491 A093492 * A093494 A093495 A093496
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 16 2004
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 12 2006
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