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

1,1

Comments

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

Links

Table of n, a(n) for n=1..12.

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

Prog

(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

Crossrefs

Cf. A007953, A034726, A034727.

Sequence in context: A232612 A339439 A266238 * A101058 A247960 A347559

Adjacent sequences: A066005 A066006 A066007 * A066009 A066010 A066011

Keyword

nonn,base

Author

N. J. A. Sloane, Dec 11 2001

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

Status

approved