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A324455
Numbers m > 1 such that there exists a divisor g > 1 of m which satisfies s_g(m) >= g.
6
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
OFFSET
1,1
COMMENTS
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.
LINKS
Bernd C. Kellner, On primary Carmichael numbers, Integers 22 (2022), Article #A38, 39 pp.; arXiv:1902.11283 [math.NT], 2019.
EXAMPLE
6 is a member, since 2 divides 6 and s_2(6) = 2.
MATHEMATICA
s[n_, g_] := If[n < 1 || g < 2, 0, Plus @@ IntegerDigits[n, g]];
f[n_] := AnyTrue[Divisors[n], s[n, #] >= # &];
Select[Range[1000], f[#] &]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernd C. Kellner, Feb 28 2019
STATUS
approved