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A357300
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a(n) is the smallest number m with exactly n divisors whose first digit equals the first digit of m.
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3
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1, 10, 100, 108, 120, 180, 1040, 1020, 1170, 1008, 1260, 1680, 10010, 10530, 10200, 10260, 10560, 10800, 11340, 10920, 12600, 10080, 15840, 18480, 15120, 102060, 104400, 101640, 100320, 102600, 100980, 117600, 114660, 107100, 174240, 113400, 105840, 100800, 120120, 143640
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OFFSET
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1,2
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COMMENTS
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a(m) <= a(551) = 18681062400 for m < 555. All terms with values up to 2*10^10 start with 1. Do there exist a(n) starting with any other digit? - Charles R Greathouse IV, Sep 25 2022
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LINKS
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EXAMPLE
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Of the twelve divisors of 108, four have their first digit equals to the first digit of 108: 1, 12, 18 and 108, and there is no such smaller number, hence a(4) = 108.
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MATHEMATICA
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f[n_] := IntegerDigits[n][[1]]; s[n_] := Module[{fn = f[n]}, DivisorSum[n, 1 &, f[#] == fn &]]; seq[len_, nmax_] := Module[{v = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = s[n]; If[i <= len && v[[i]] == 0, c++; v[[i]] = n]; n++]; v]; seq[40, 10^6] (* Amiram Eldar, Sep 23 2022 *)
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PROG
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(PARI) f(n) = my(fd=digits(n)[1]); sumdiv(n, d, digits(d)[1] == fd); \\ A357299
a(n) = my(k=1); while (f(k)!=n, k++); k; \\ Michel Marcus, Sep 23 2022
(PARI) v=vector(1000); v[1]=r=1; forfactored(n=2, 10^11, t=a(n[1], n[2], r); if(t>r && v[t]==0, v[t]=n[1]; print(t" "n[1]" = "n[2]); while(v[r], r++); r--)) \\ Charles R Greathouse IV, Sep 25 2022
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CROSSREFS
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Similar, but with: A333456 (Niven numbers), A335038 (Zuckerman numbers).
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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