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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
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
1,1
COMMENTS
A generalization of Ruth-Aaron pairs (A006145).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
FORMULA
sopfr(k+1) mod sopfr(k) = 0.
EXAMPLE
a(6)=160 since sopfr(160)=sopfr(2^5*5)=10+5=15 and sopfr(161)=sopfr(7*23)=30.
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Walter Kehowski, Apr 09 2007
STATUS
approved