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Numbers n such that sopf(n) = sopf(n+1) - sopf(n-1), where sopf(x) = sum of the distinct prime factors of x.
8

%I #11 Sep 08 2022 08:45:07

%S 4,22,57,900,1551,1920,4194,6279,10857,19648,20384,32016,63656,65703,

%T 83271,84119,86241,105570,145237,181844,271328,271741,316710,322953,

%U 331976,345185,379659,381430,409915,424503,490255,524476,542565,550271

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

%H Amiram Eldar, <a href="/A076525/b076525.txt">Table of n, a(n) for n = 1..10000</a>

%e The sum of the distinct prime factors of 22 is 2 + 11 = 13; the sum of the distinct prime factors of 23 is 23; the sum of the distinct prime factors of 21 is 3 + 7 = 10; and 13 = 23 - 10. Hence 22 belongs to the sequence.

%t p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^5], p[ # ] == p[ # + 1] - p[ # - 1] &]

%o (Magma) [k:k in [3..560000]| &+PrimeDivisors(k) eq &+PrimeDivisors(k+1)-&+PrimeDivisors(k-1)]; // _Marius A. Burtea_, Oct 10 2019

%Y Cf. A008472, A075565, A075784, A075846, A076527, 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