OFFSET
1,1
EXAMPLE
792007675 is a term since 792007675 = 2^2 * 31680307, 792007675 + 1 = 792007676 = 2^2 * 198001919, 792007675 + 2 = 792007677 = 3^2 * 88000853, 792007675 + 3 = 792007678 = 2 * 7^2 * 11^2 * 66791 and 792007675 + 4 = 792007679 = 17^2 * 2740511 all have an equal number of even and odd exponents in their prime factorization.
MATHEMATICA
q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), _?OddQ] == Count[e, _?EvenQ]; v = q /@ Range[5]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 4]], {k, 6, 3*10^9}]; seq
PROG
(Python)
from sympy import factorint
def cond(n):
evenodd = [0, 0]
for e in factorint(n).values():
evenodd[e%2] += 1
return evenodd[0] == evenodd[1]
def afind(limit, startk=6):
condvec = [cond(startk+i) for i in range(5)]
for kp4 in range(startk+4, limit+5):
condvec = condvec[1:] + [cond(kp4)]
if all(condvec):
print(kp4-4, end=", ")
afind(10**9) # Michael S. Branicky, Sep 27 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 27 2021
STATUS
approved