%I #21 Feb 24 2023 11:53:57

%S 1,3,3,7,1,3,11,11,1,3,11,23,51,43,43,87,23,47,15,95,215,431,47,47,

%T 295,423,391,783,143,287,1311,1887,847,719,719,1439,3471,2511,975,

%U 1951,7583,15167,14655,12607,4383,8767,575,575,16959,25407,24895,49791,639,10879

%N Read (exponents of primes in the factorization of n!) modulo 2 and convert to decimal.

%H David A. Corneth, <a href="/A240504/b240504.txt">Table of n, a(n) for n = 2..10000</a>

%e Since 9! = 2^7*3^4*5*7, then we have a binary number the digits of which are the exponents modulo 2: 1011. In decimal this is 11. So a(9)=11.

%o (PARI) a(n) = subst(Pol(factor(n!)[,2] % 2), x, 2); \\ _Michel Marcus_, Feb 15 2016

%o (PARI) a(n) = { my(res = 0); forprime(p = 2, n, res = 2*res + (val(n, p)%2) ); res }

%o val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Feb 24 2023

%Y Cf. A055204, A240502, A336510.

%K nonn,base

%O 2,2

%A _Vladimir Shevelev_, Apr 06 2014

%E More terms from _Michel Marcus_, Feb 15 2016