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A076624
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Sum of the non-divisors of n between 1 and n is a perfect square.
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0
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1, 2, 5, 6, 14, 149, 158, 384, 846, 5065, 8648, 181166, 196366, 947545, 5821349, 55867168, 491372910, 4273496001, 40534401950, 87226316289
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OFFSET
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1,2
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COMMENTS
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Define b(0)=2, b(1)=5 and b(n)=6*b(n-1)-b(n-2)-2 for n>1. A prime number p is in the sequence iff (p^2-p-2)/2 is a square iff p=b(n) for some n. The next prime in the sequence is b(21)=8946229758127349, followed by b(n) for n=33, 51, 57 and 75.
a(21) > 2*10^11. - Donovan Johnson, Jul 09 2011
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LINKS
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FORMULA
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EXAMPLE
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The sum of the non-divisors of 14 between 1 and 14 is 3 + 4 + 5 + 6 + 8 + 9 + 10 + 11 + 12 + 13 = 81 = 9^2. 1, 2, 7 & 14 are divisors. Hence 14 is a term of the sequence.
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MATHEMATICA
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Select[ Range[14*10^6], IntegerQ[Sqrt[(# (# + 1)/2) - DivisorSigma[1, # ]]] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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