

A348076


Number k such that k and k+1 both have an equal number of even and odd exponents in their prime factorization (A187039).


5



44, 75, 98, 116, 147, 171, 175, 207, 244, 332, 368, 387, 404, 507, 548, 603, 604, 656, 724, 800, 832, 844, 847, 891, 908, 931, 963, 1052, 1075, 1083, 1124, 1250, 1251, 1323, 1324, 1412, 1467, 1556, 1587, 1675, 1772, 1791, 2096, 2224, 2312, 2348, 2367, 2511, 2523
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

44 is a term since 44 = 2^2 * 11 and 44 + 1 = 45 = 3^2 * 5 both 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]; Select[Range[2500], q[#] && q[# + 1] &]


PROG

(Python)
from sympy import factorint
def aupto(limit):
alst, cond = [], False
for nxtk in range(3, limit+2):
evenodd = [0, 0]
for e in factorint(nxtk).values():
evenodd[e%2] += 1
nxtcond = (evenodd[0] == evenodd[1])
if cond and nxtcond:
alst.append(nxtk1)
cond = nxtcond
return alst


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



