A240504 Read (exponents of primes in the factorization of n!) modulo 2 and convert to decimal.
1, 3, 3, 7, 1, 3, 11, 11, 1, 3, 11, 23, 51, 43, 43, 87, 23, 47, 15, 95, 215, 431, 47, 47, 295, 423, 391, 783, 143, 287, 1311, 1887, 847, 719, 719, 1439, 3471, 2511, 975, 1951, 7583, 15167, 14655, 12607, 4383, 8767, 575, 575, 16959, 25407, 24895, 49791, 639, 10879
Offset: 2
Examples
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.
Links
- David A. Corneth, Table of n, a(n) for n = 2..10000
Programs
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PARI
a(n) = subst(Pol(factor(n!)[,2] % 2), x, 2); \\ Michel Marcus, Feb 15 2016
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PARI
a(n) = { my(res = 0); forprime(p = 2, n, res = 2*res + (val(n, p)%2) ); res } val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Feb 24 2023
Extensions
More terms from Michel Marcus, Feb 15 2016