A113315 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

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