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A349189
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Number of n-phobe numbers.
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1
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OFFSET
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2,1
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COMMENTS
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A n-phile integer m is such that there are n positive integers b_1 < b_2 < ... < b_j < ... < b_n with the property that b_1 divides b_2, b_2 divides b_3, ..., b_[j-1] divides b_j, ..., b_[n-1] divides b_n, and m = b_1 + b_2 + ... + b_j + ... + b_n. A number that is not n-phile is called n-phobe.
The words 'n-phile' and 'n-phobe' come from the French website Diophante (see link).
The number of n-phobe numbers is always finite, the smallest one is always 1 and the largest n-phobe number is in A349188.
a(6) >= 177, a(7) >= 459, a(8) >= 1162, a(9) >= 2947. - David A. Corneth, Nov 15 2021
Indeed, all these bounds are the corresponding values of a(6), a(7), a(8) and a(9). Proof comes from Proof link in A349188. - Bernard Schott, Nov 19 2021
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LINKS
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EXAMPLE
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For n = 2, integers 1 and 2 are 2-phobe, then for m >= 3, every m = 1 + (m-1) with 1 < m-1 and 1 divides m-1, so, each m >= 3 is 2-phile number and a(2) = 2.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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