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A125286
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a(0)=1. a(n) = a(n-1) + (the largest term among {a(0),a(1),...a(n-1)} that has the same number of positive divisors as n).
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0
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1, 2, 4, 6, 10, 12, 22, 24, 46, 50, 96, 98, 196, 198, 244, 290
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OFFSET
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0,2
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COMMENTS
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a(16) does not exist because no earlier term has exactly 5 divisors. However, arbitrary modifications of the sequence's definition (such as letting a(n) = a(n-1) + 0 if no earlier term has the same number of divisors as n, or letting a(n) = a(n-1) + the largest earlier term with at most n divisors, etc.) would allow the sequence to be infinite in length.
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LINKS
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EXAMPLE
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9 has 3 divisors. So a(9) = a(8) + the largest earlier term with 3 divisors. a(3) = 4 is the only earlier term with 3 divisors, so a(9) = a(8) + 4 = 50.
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CROSSREFS
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KEYWORD
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fini,full,nonn
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AUTHOR
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STATUS
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approved
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