A129316 Positive integers k such that sopfr(k) divides sopfr(k+1), where sopfr(k) is the sum of the prime factors of k, counting multiplicity.

5, 8, 15, 77, 125, 160, 252, 496, 714, 948, 980, 1045, 1053, 1260, 1330, 1378, 1404, 1430, 1508, 1520, 1610, 1750, 1862, 1890, 2170, 2491, 2680, 2821, 3094, 3100, 3248, 3400, 3591, 3610, 3652, 3808, 4185, 4191, 4384, 4452, 4500, 4598, 4906, 5120, 5145

Offset: 1

Author

Walter Kehowski, Apr 09 2007

Keywords

• easy
• nonn

Comments

A generalization of Ruth-Aaron pairs (A006145).

Examples

			a(6)=160 since sopfr(160)=sopfr(2^5*5)=10+5=15 and sopfr(161)=sopfr(7*23)=30.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A001414, A006145, A039752, A129317, A129318, A129319.

Programs

Mathematica

sopf[n_]:=Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[n]]]; Rest[ Flatten[Position[Partition[Table[sopf[n],{n,5200}],2,1],?(Divisible[#[[2]],#[[1]]]&),{1},Heads->False]]] (* _Harvey P. Dale, Jul 18 2013 *)

Formula

sopfr(k+1) mod sopfr(k) = 0.