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%I #8 Aug 07 2022 07:53:19
%S 819,1035,1196,1274,1275,1449,1665,1924,1925,1988,2324,2331,2540,3068,
%T 3195,3324,3339,3549,3555,3626,3717,4164,4220,4235,4556,4598,4635,
%U 4675,4796,5084,5525,5634,5660,6003,6027,6068,6164,6363,6740,6867,6908,7028,7227,7275
%N Number k such that k and k+1 both have an equal sum of even and odd exponents in their prime factorization (A356413).
%C Numbers k such that A350386(k) = A350387(k) and A350386(k+1) = A350387(k+1).
%H Amiram Eldar, <a href="/A356414/b356414.txt">Table of n, a(n) for n = 1..10000</a>
%e 819 is a term since A350386(819) = A350387(819) = 2 and A350386(820) = A350387(820) = 2.
%t f[p_, e_] := (-1)^e*e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; Select[Range[10^4], q[#] && q[# + 1] &]
%o (PARI) is(n) = {my(f = factor(n)); sum(i = 1, #f~, (-1)^f[i,2]*f[i,2]) == 0};
%o is1 = is(1); for(k = 2, 10^4, is2 = is(k); if(is1 && is2, print1(k-1,", ")); is1 = is2);
%Y Cf. A350386, A350387, A356413.
%K nonn
%O 1,1
%A _Amiram Eldar_, Aug 06 2022
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