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A324455
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Numbers m > 1 such that there exists a divisor g > 1 of m which satisfies s_g(m) >= g.
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6
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6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105
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OFFSET
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1,1
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COMMENTS
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The function s_g(m) gives the sum of the base-g digits of m.
The sequence is infinite, since it contains A324460 and the Carmichael numbers A002997.
A term m must have at least 2 prime factors, and the divisor g satisfies the inequalities 1 < g < m^(1/(ord_g(m)+1)) <= sqrt(m), where ord_g(m) gives the maximum exponent e such that g^e divides m.
See Kellner 2019.
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LINKS
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EXAMPLE
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6 is a member, since 2 divides 6 and s_2(6) = 2.
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MATHEMATICA
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s[n_, g_] := If[n < 1 || g < 2, 0, Plus @@ IntegerDigits[n, g]];
f[n_] := AnyTrue[Divisors[n], s[n, #] >= # &];
Select[Range[1000], f[#] &]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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