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A076527
Numbers n such that sopf(n) = sopf(n-1) - sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.
8
8, 66, 2883, 3264, 3552, 13872, 21386, 26896, 29698, 29768, 31980, 36567, 40517, 65305, 72012, 82719, 101639, 110848, 160230, 211646, 237136, 237568, 238303, 242606, 299186, 309960, 378014, 393208, 439105, 445795, 455182, 527078, 570021
OFFSET
1,1
LINKS
EXAMPLE
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.
MATHEMATICA
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # ] == p[ # - 1] - p[ # - 2] &]
PROG
(Magma) [k:k in [4..571000]| &+PrimeDivisors(k-1) - &+PrimeDivisors(k-2) eq (&+PrimeDivisors(k))]; // Marius A. Burtea, Feb 12 2020
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 18 2002
EXTENSIONS
Edited and extended by Ray Chandler, Feb 13 2005
STATUS
approved