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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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A092544 A319087 A098499 * A075707 A126420 A246607
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 18 2002
EXTENSIONS
Edited and extended by Ray Chandler, Feb 13 2005
STATUS
approved

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Last modified June 24 11:50 EDT 2024. Contains 373677 sequences. (Running on oeis4.)