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A086706
Number of Niven numbers less than or equal to n.
2
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
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
KEYWORD
nonn,base
AUTHOR
Benoit Cloitre, Jul 28 2003
STATUS
approved