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.

9, 23, 180, 1325, 10334, 83556, 710667, 6148698, 54619717, 491432596, 4471325309, 40951585117

Offset: 1

Author

N. J. A. Sloane, Dec 11 2001

Keywords

• nonn
• base

Comments

Harshad numbers were named by D. Kaprekar; the word "harshad" in Sanskrit means "giving joy." - Harvey P. Dale, Nov 08 2011

Links

• S. W. Golomb, Sums and products of digits, IEEE Information Theory Society Newsletter, 51 (No. 3, Sept. 2001), p. 15.

Crossrefs

Cf. A007953, A034726, A034727.

Programs

ARIBAS

: 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).

Python

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

Extensions

One more term from Klaus Brockhaus, Dec 12 2001

a(9)-a(12) from Donovan Johnson, Mar 10 2010

Definition expanded by Harvey P. Dale, Nov 08 2011