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A129316 Positive integers n such that sopfr(n) divides sopfr(n+1), where sopfr(n) is the sum of the prime factors of n, counting multiplicity. A generalization of Ruth-Aaron pairs (A006145). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

sopfr(n+1) mod sopfr(n) = 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

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Last modified January 20 04:43 EST 2019. Contains 319323 sequences. (Running on oeis4.)