A086706 Number of Niven numbers less than or equal to n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 27, 27, 28

Offset: 1

Author

Benoit Cloitre, Jul 28 2003

Keywords

• nonn
• base

Comments

Niven numbers are also known as harshad numbers. - Harvey P. Dale, May 20 2021

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Jean-Marie De Koninck and Nicolas Doyon, Large and Small Gaps Between Consecutive Niven Numbers, J. Integer Seqs., Vol. 6, 2003, Article 03.2.5.

Crossrefs

Cf. A005349.

Partial sums of A188641.

Programs

Mathematica

Accumulate[Table[If[Divisible[n,Total[IntegerDigits[n]]],1,0],{n,80}]] (* Harvey P. Dale, May 20 2021 *)

PARI

s(k)=if(k<1,0,if(k%10,s(k-1)+1,s(k/10)));
a(n)=sum(k=1,n,if(k%s(k),0,1));

Formula

a(n) = (c+o(1))*n/log(n) where c = 14/27*log(10) = 1.1939330111820977620834029765030036632....