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A075565 Numbers n such that sopf(n) = sopf(n-1) + sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.

%I A075565 #29 Sep 08 2022 08:45:07
%S A075565 5,23,58,901,1552,1921,4195,6280,10858,19649,20385,32017,63657,65704,
%T A075565 83272,84120,86242,105571,145238,181845,271329,271742,316711,322954,
%U A075565 331977,345186,379660,381431,409916,424504,490256,524477,542566,550272,561661,565217,566560
%N A075565 Numbers n such that sopf(n) = sopf(n-1) + sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.
%H A075565 Amiram Eldar, <a href="/A075565/b075565.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..371 from G. C. Greubel)
%e A075565 The sum of the distinct prime factors of 23 is 23; the sum of the distinct prime factors of 22 = 2 * 11 is 2 + 11 = 13; the sum of the distinct prime factors of 21 = 3 * 7 is 3 + 7 = 10; Hence 23 belongs to the sequence.
%t A075565 p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # - 1] + p[ # - 2] == p[ # ] &]
%o A075565 (PARI) sopf(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]);
%o A075565 isok(n) = sopf(n) == sopf(n-1) + sopf(n-2); \\ _Michel Marcus_, Feb 12 2020
%o A075565 (Magma) [k:k in [5..560000]| &+PrimeDivisors(k-1)+ &+PrimeDivisors(k-2) eq &+PrimeDivisors(k)]; // _Marius A. Burtea_, Feb 12 2020
%o A075565 (Python)
%o A075565 from sympy import primefactors
%o A075565 def sopf(n): return sum(primefactors(n))
%o A075565 def afind(limit):
%o A075565   sopfm2, sopfm1, sopf = 2, 3, 2
%o A075565   for k in range(4, limit+1):
%o A075565     if sopf == sopfm1 + sopfm2: print(k, end=", ")
%o A075565     sopfm2, sopfm1, sopf = sopfm1, sopf, sum(primefactors(k+1))
%o A075565 afind(600000) # _Michael S. Branicky_, May 23 2021
%Y A075565 Cf. A008472, A075784, A075846, A076525, A076527, A076531, A076532, A076533.
%K A075565 nonn
%O A075565 1,1
%A A075565 _Joseph L. Pe_, Oct 18 2002
%E A075565 Edited and extended by _Ray Chandler_, Feb 13 2005