%I #15 Sep 08 2022 08:45:07
%S 8,66,2883,3264,3552,13872,21386,26896,29698,29768,31980,36567,40517,
%T 65305,72012,82719,101639,110848,160230,211646,237136,237568,238303,
%U 242606,299186,309960,378014,393208,439105,445795,455182,527078,570021
%N Numbers n such that sopf(n) = sopf(n-1) - sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.
%H Amiram Eldar, <a href="/A076527/b076527.txt">Table of n, a(n) for n = 1..10000</a>
%e The sum of the distinct prime factors of 66 is 2 + 3 + 11 = 16; the sum of the distinct prime factors of 65 is 5 + 13 = 18; the sum of the distinct prime factors of 64 is 2; and 16 = 18 - 2. Hence 66 belongs to the sequence.
%t p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # ] == p[ # - 1] - p[ # - 2] &]
%o (Magma) [k:k in [4..571000]| &+PrimeDivisors(k-1) - &+PrimeDivisors(k-2) eq (&+PrimeDivisors(k))]; // _Marius A. Burtea_, Feb 12 2020
%Y Cf. A008472, A075565, A075784, A075846, A076525, A076531, A076532, A076533.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Oct 18 2002
%E Edited and extended by _Ray Chandler_, Feb 13 2005