A129316 - OEIS

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

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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

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

Sequence in context: A259585 A220034 A063731 * A039752 A141536 A314561

Adjacent sequences: A129313 A129314 A129315 * A129317 A129318 A129319

KEYWORD

easy,nonn

AUTHOR

Walter Kehowski, Apr 09 2007

STATUS

approved