A219340 Numbers not multiples of 9 whose digital sum coincides with digital sum of their largest proper divisor.

361, 551, 703, 1007, 1273, 1691, 1843, 2033, 2071, 2183, 2413, 2603, 2641, 2701, 2831, 2923, 3071, 3173, 3293, 3743, 3781, 4033, 4313, 4351, 4541, 5143, 5263, 5513, 6023, 6031, 6401, 6403, 6623, 6631, 6821, 7081, 7141, 7363, 7391, 7543, 8303, 8341, 8531

Offset

1,1

Comments

The number n has a prime factor of the form 18k+1.

Links

Antonio Roldán and T. D. Noe, Table of n, a(n) for n = 1..10000 (542 terms from Antonio Roldán)

Example

12673 is in the sequence because 12673 = 19*23*29, their largest proper divisor is 667. Both have a digital sum of 19.

Mathematica

Select[Range[2, 10000], Mod[#, 9] > 0 && Total[IntegerDigits[#]] == Total[IntegerDigits[Divisors[#][[-2]]]] &] (* T. D. Noe, Nov 20 2012 *)

Prog

(PARI) largdiv(n)=if(n==1, 1, n/factor(n)[1, 1]) /* Charles R Greathouse IV, Jun 15 2011 */
  digsum(n)={local (d, p); d=0; p=n; while(p, d+=p%10; p=floor(p/10)); return(d)}
{ k=0; for (n=2, 10^5,  if(digsum(n)==digsum(largdiv(n))&&n%9>0, k=k+1; write("B219340.txt", k, ", ", n))); } /* Antonio Roldán, Nov 18 2012 */

Crossrefs

Sequence in context: A367792 A325882 A255787 * A183997 A211822 A233552

Adjacent sequences: A219337 A219338 A219339 * A219341 A219342 A219343

Keyword

nonn,base

Author

Antonio Roldán, Nov 18 2012

Status

approved