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

1,2

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.

Formula

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

Mathematica

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

Prog

(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));

Crossrefs

Cf. A005349.

Partial sums of A188641.

Sequence in context: A367366 A285757 A136687 * A100470 A071604 A337769

Adjacent sequences: A086703 A086704 A086705 * A086707 A086708 A086709

Keyword

nonn,base

Author

Benoit Cloitre, Jul 28 2003

Status

approved