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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.
15
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
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..371 from G. C. Greubel)
EXAMPLE
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.
MATHEMATICA
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # - 1] + p[ # - 2] == p[ # ] &]
PROG
(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))
afind(600000) # Michael S. Branicky, May 23 2021
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 18 2002
EXTENSIONS
Edited and extended by Ray Chandler, Feb 13 2005
STATUS
approved