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A083890
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Number of divisors of n with largest digit = 3 (base 10).
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12
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1
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OFFSET
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1,30
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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/A277965(k) = 0.84217457724798904648... . - Amiram Eldar, Jan 04 2024
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EXAMPLE
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n=132, 3 of the 12 divisors of 132 have largest digit =3: {3,33,132}, therefore a(132)=3.
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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:= 3:
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MATHEMATICA
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With[{k = 3}, Array[DivisorSum[#, 1 &, And[#[[k]] > 0, Total@ #[[k + 1 ;; 9]] == 0] &@ DigitCount[#] &] &, 105]] (* Michael De Vlieger, Oct 06 2019 *)
Table[Count[Divisors[n], _?(Max[IntegerDigits[#]]==3&)], {n, 120}] (* Harvey P. Dale, Sep 05 2020 *)
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PROG
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(Magma) [#[d:d in Divisors(n) | Max(Intseq(d)) eq 3]: n in [1..130]]; // Marius A. Burtea, Oct 06 2019
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CROSSREFS
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Cf. A054055, A000005, A083898, A083888, A083889, A083891, A083892, A083893, A083894, A083895, A083896, A277965.
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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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