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A219340 Numbers not multiples of 9 whose digital sum coincides with digital sum of their largest proper divisor. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A003930 A137607 A255787 * A183997 A211822 A233552

Adjacent sequences:  A219337 A219338 A219339 * A219341 A219342 A219343

KEYWORD

nonn,base

AUTHOR

Antonio Roldán, Nov 18 2012

STATUS

approved

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Last modified June 27 13:28 EDT 2017. Contains 288788 sequences.