A034727
a(n) = that n-digit number m which gives minimal integral value of m/(sum of digits of m); in case of a tie pick the smallest.
Original entry on oeis.org
1, 18, 198, 1098, 10989, 109888, 1078999, 10998988, 109989999, 1078999989, 10999999989, 108999999989, 1098999999999, 10899899999998, 104999999999999, 1018899999999999, 10199998999999998, 100999999999999988
Offset: 1
A066007
a(n) is that n-digit number m which minimizes m/(sum of digits of m); in case of a tie pick the smallest.
Original entry on oeis.org
1, 19, 199, 1099, 10999, 109999, 1099999, 10999999, 109999999, 1099999999, 10999999999, 109999999999, 1099999999999, 10999999999999, 100999999999999, 1009999999999999, 10099999999999999, 100999999999999999, 1009999999999999999, 10099999999999999999
Offset: 1
- S. W. Golomb, Sums and products of digits, IEEE Information Theory Society Newsletter, 51 (No. 3, Sept. 2001), p. 15.
- S. W. Golomb, Sums and Products of Digits Solutions, IEEE Information Theory Society Newsletter, Vol. 67, No. 1, March 2017, p. 22. Reprint.
A066008
Number of n-digit positive integers m for which m/(sum of digits of m) is an integer, sometimes referred to as Niven or Harshad numbers.
Original entry on oeis.org
9, 23, 180, 1325, 10334, 83556, 710667, 6148698, 54619717, 491432596, 4471325309, 40951585117
Offset: 1
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: function a066008(a,b: integer); var n,c,m,j,k: integer; s: string; begin for n := a to b do c := 0; for m := 10^n to 10^(n+1) - 1 do s := itoa(m); k := 0; for j := 0 to length(s) - 1 do k := k + atoi(s[j..j]); end; if m mod k = 0 then inc(c); end; end; write(c,","); end; return; end; a066008(0,7).
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def sd(m): return sum(map(int, str(m)))
def is_harshad(m): return m > 0 and m%sd(m) == 0
def a(n): return sum(is_harshad(m) for m in range(10**(n-1), 10**n))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Sep 23 2021
Original entry on oeis.org
1, 9, 18, 18, 27, 34, 43, 52, 63, 69, 81, 89, 99, 106, 113, 117, 126, 134, 147
Offset: 1
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