

A348077


Starts of runs of 3 consecutive numbers that have an equal number of even and odd exponents in their prime factorization (A187039).


3



603, 1250, 1323, 2523, 4203, 4923, 4948, 7442, 10467, 12591, 18027, 20402, 21123, 23823, 31507, 31850, 36162, 40327, 54475, 54511, 55323, 58923, 63747, 64386, 71523, 73204, 79011, 83151, 85291, 88047, 97675, 103923, 104211, 118323, 120787, 122571, 124891, 126927
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OFFSET

1,1


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

603 is a term since 603 = 3^2 * 67, 603 + 1 = 604 = 2^2 * 151 and 603 + 2 = 605 = 5 * 11^2 all have one even and one odd exponent in their prime factorization.


MATHEMATICA

q[n_] := n == 1  Count[(e = FactorInteger[n][[;; , 2]]), _?OddQ] == Count[e, _?EvenQ]; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k  2]], {k, 4, 130000}]; seq


PROG

(Python)
from sympy import factorint
def aupto(limit):
alst, condvec = [], [False, False, False]
for kp2 in range(4, limit+3):
evenodd = [0, 0]
for e in factorint(kp2).values():
evenodd[e%2] += 1
condvec = condvec[1:] + [evenodd[0] == evenodd[1]]
if all(condvec):
alst.append(kp22)
return alst
print(aupto(126927)) # Michael S. Branicky, Sep 27 2021


CROSSREFS

Subsequence of A187039 and A348076.
Sequence in context: A218521 A145331 A252957 * A066785 A178032 A107256
Adjacent sequences: A348074 A348075 A348076 * A348078 A348079 A348080


KEYWORD

nonn


AUTHOR

Amiram Eldar, Sep 27 2021


STATUS

approved



