OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Harvey P. Dale)
EXAMPLE
The sum of the distinct prime factors of 21 is 3 + 7 = 10; the sum of the distinct prime factors of 22 is 2 + 11 = 13; the sum of the distinct prime factors of 20 is 2 + 5 = 7; and 10 = (1/2)*(13 + 7). Hence 21 belongs to the sequence.
MATHEMATICA
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^5], p[ # ] == 0.5 (p[ # + 1] + p[ # - 1]) &]
sopf[n_]:=Total[Transpose[FactorInteger[n]][[1]]]; Rest[Flatten[ Position[ Partition[sopf/@Range[650000], 3, 1], _?(Mean[{First[ #], Last[#]}] == #[[2]]&), {1}, Heads->False]]]+1 (* Harvey P. Dale, Sep 05 2013 *)
PROG
(Magma) [k:k in [3..642000]| (1/2)*(&+PrimeDivisors(k+1) + &+PrimeDivisors(k-1)) eq (&+PrimeDivisors(k))]; // Marius A. Burtea, Feb 12 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 18 2002
EXTENSIONS
Edited and extended by Ray Chandler, Feb 13 2005
STATUS
approved