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A083888
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Number of divisors of n with largest digit = 1 (base 10).
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11
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1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1
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OFFSET
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1,10
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A007088(k) = 1.23840561530559480971.... -Amiram Eldar,Jan 04 2024
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EXAMPLE
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n=110, 4 of the divisors of 110 {1,2,5,10,11,22,55,110} have largest digit =1: {1,10,11,110}, therefore a(110)=4.
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MAPLE
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f:= proc(n) nops(select(t -> max(convert(t, base, 10))=d, numtheory:-divisors(n))) end proc:
d:= 1:
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MATHEMATICA
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With[{k = 1}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (*Michael De Vlieger,Oct 06 2019 *)
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PROG
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(Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 1]: n in [1..110]]; //Marius A. Burtea,Oct 06 2019
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CROSSREFS
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Cf.A054055,A000005,A007088,A083889,A083890,A083891,A083892,A083893,A083894,A083895,A083896.
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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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