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A075565
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Numbers n such that sopf(n) = sopf(n-1) + sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.
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15
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5, 23, 58, 901, 1552, 1921, 4195, 6280, 10858, 19649, 20385, 32017, 63657, 65704, 83272, 84120, 86242, 105571, 145238, 181845, 271329, 271742, 316711, 322954, 331977, 345186, 379660, 381431, 409916, 424504, 490256, 524477, 542566, 550272, 561661, 565217, 566560
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # - 1] + p[ # - 2] == p[ # ] &]
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PROG
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(PARI) sopf(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]);
isok(n) = sopf(n) == sopf(n-1) + sopf(n-2); \\ Michel Marcus, Feb 12 2020
(Magma) [k:k in [5..560000]| &+PrimeDivisors(k-1)+ &+PrimeDivisors(k-2) eq &+PrimeDivisors(k)]; // Marius A. Burtea, Feb 12 2020
(Python)
from sympy import primefactors
def sopf(n): return sum(primefactors(n))
def afind(limit):
sopfm2, sopfm1, sopf = 2, 3, 2
for k in range(4, limit+1):
if sopf == sopfm1 + sopfm2: print(k, end=", ")
sopfm2, sopfm1, sopf = sopfm1, sopf, sum(primefactors(k+1))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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