A113315 Niven (or Harshad) numbers A005349 divided by the sum of their digits.

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 4, 2, 10, 7, 4, 3, 10, 4, 10, 7, 5, 4, 10, 6, 10, 7, 10, 8, 10, 9, 7, 10, 100, 34, 12, 55, 37, 28, 19, 13, 40, 14, 22, 19, 15, 28, 16, 25, 19, 17, 13, 18, 19, 20, 19, 16, 13, 11, 100, 67, 34, 23, 19, 70, 24, 55, 37, 28, 25, 19, 46, 26, 40, 27, 19, 28, 29

Offset: 1

Author

Amarnath Murthy, Dec 20 2001

Keywords

• nonn
• base

Comments

a(n)=10234 is particularly frequent, it is obtained by the following integers: 102340, 133042, 153510, 184212, 204680, 214914, 225148, 235382, 245616, 255850, 266084, 276318, 286552, 327488, 347956, 378658, 388892,.... Carmine Suriano, May 04 2013

Examples

			12 is the 11th term of A005349, hence a(11) = 12/(1+2) = 4.
		

Links

• Carmine Suriano, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005349 (Niven (or Harshad) numbers: numbers that are divisible by the sum of their digits). Cf. also A066355.

Programs

Mathematica

Select[# / DigitSum[#] & /@ Range[300], IntegerQ] (* Amiram Eldar, May 26 2024 *)

PARI

lista(nn) = {for (i = 1, nn, if (i % sumdigits(i) == 0, print1(i/sumdigits(i), ", ")););} \\ Michel Marcus, Oct 09 2013

Formula

a(n) = A005349(n)/A007953(A005349(n)). - Michel Marcus, Oct 09 2013

Extensions

Corrected, extended and edited by Zak Seidov, Oct 26 2005