A064675 Numbers k such that sopfr(k) = sopf(k+1), where sopf(k) = A008472(k) and sopfr(k) = A001414(k).

5, 27, 77, 714, 836, 948, 1449, 4185, 4624, 5405, 5560, 8476, 8855, 10175, 16932, 17080, 18655, 20450, 20600, 21183, 26642, 28809, 31524, 35631, 37828, 37881, 40081, 47544, 48203, 49240, 52155, 52554, 53192, 63344, 63426, 63665, 79118, 80800, 81576, 83780

Offset: 1

Author

Jason Earls, Oct 10 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from Harry J. Smith)

Crossrefs

Cf. A001414 (sopfr), A008472 (sopf).

Programs

PARI

sopf(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s) }
sopfr(n)= { local(f,s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]*f[i, 2]); return(s) }
{ n=0; for (m=1, 10^9, if (sopfr(m)==sopf(m + 1), write("b064675.txt", n++, " ", m); if (n==500, break)) ) } \\ Harry J. Smith, Sep 21 2009

Python

from sympy import factorint
def aupton(terms):
  alst, k, sopfk, sopfrk, sopfkp1, sopfrkp1 = [], 2, 2, 3, 2, 3
  while len(alst) < terms:
    if sopfrk == sopfkp1: alst.append(k)
    k += 1
    fkp1 = factorint(k+1)
    sopfk, sopfkp1 = sopfkp1, sum(p for p in fkp1)
    sopfrk, sopfrkp1 = sopfrkp1, sum(p*fkp1[p] for p in fkp1)
  return alst
print(aupton(40)) # Michael S. Branicky, May 27 2021