A075565 Numbers n such that sopf(n) = sopf(n-1) + sopf(n-2), where sopf(x) = sum of the distinct prime factors of x.

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

Author

Joseph L. Pe, Oct 18 2002

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..371 from G. C. Greubel)

Crossrefs

Cf. A008472, A075784, A075846, A076525, A076527, A076531, A076532, A076533.

Programs

Magma

[k:k in [5..560000]| &+PrimeDivisors(k-1)+ &+PrimeDivisors(k-2) eq &+PrimeDivisors(k)]; // Marius A. Burtea, Feb 12 2020

Mathematica

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[4, 10^5], p[ # - 1] + p[ # - 2] == p[ # ] &]

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

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

Extensions

Edited and extended by Ray Chandler, Feb 13 2005