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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 (list; graph; refs; listen; history; text; internal format)
 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, Table of n, a(n) for n = 1..743 Bernd C. Kellner, On primary Carmichael numbers, 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 Subsequences are A002997, A324315, A324316, A324456, A324457, A324458, A324459, A324460. Sequence in context: A323304 A325411 A106543 * A327476 A007774 A030231 Adjacent sequences: A324452 A324453 A324454 * A324456 A324457 A324458 KEYWORD nonn,base AUTHOR Bernd C. Kellner, Feb 28 2019 STATUS approved

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Last modified September 10 09:32 EDT 2024. Contains 375786 sequences. (Running on oeis4.)