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Number of Niven numbers less than or equal to n.
2

%I #22 Jun 25 2022 01:41:33

%S 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,

%T 16,16,16,17,17,17,17,17,17,18,18,18,18,19,19,20,20,20,21,21,21,22,22,

%U 23,23,23,23,24,24,24,24,24,24,25,25,25,26,26,26,26,26,26,26,27,27,28

%N Number of Niven numbers less than or equal to n.

%C Niven numbers are also known as harshad numbers. - _Harvey P. Dale_, May 20 2021

%H Harvey P. Dale, <a href="/A086706/b086706.txt">Table of n, a(n) for n = 1..1000</a>

%H Jean-Marie De Koninck and Nicolas Doyon, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.html">Large and Small Gaps Between Consecutive Niven Numbers</a>, J. Integer Seqs., Vol. 6, 2003, Article 03.2.5.

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

%t Accumulate[Table[If[Divisible[n,Total[IntegerDigits[n]]],1,0],{n,80}]] (* _Harvey P. Dale_, May 20 2021 *)

%o (PARI)

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

%o a(n)=sum(k=1,n,if(k%s(k),0,1));

%Y Cf. A005349.

%Y Partial sums of A188641.

%K nonn,base

%O 1,2

%A _Benoit Cloitre_, Jul 28 2003