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

Author

Antonio Roldán, Nov 18 2012

Keywords

• nonn
• base
• changed

Comments

Terms have a prime factor of the form 18*k+1.

Examples

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

Links

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

Crossrefs

Cf. A032742.

Programs

Mathematica

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

PARI

largdiv(n)=if(n==1, 1, n/factor(n)[1, 1]) \\ A032742
isok(n) = n>1 && sumdigits(n)==sumdigits(largdiv(n)) && n%9>0
select(isok, [1..10000]) /* Antonio Roldán, Nov 18 2012 */